Improve Tuition · GCSE Maths · Grade 3 · 100-question paper
Lesson 23 · Angles · Grade 3 lock

Angles — 100 Questions

Five bands, easy to hardest, all within Grade 3.

100 marks · 5 sections · grade-locked (no Grade 4+ techniques required)

Name:Date:Score: / 100
Grade-locked: every question can be solved with the six angle facts on the lesson page (line, point, vertically opposite, triangle, quadrilateral, parallel lines). No exterior-angle theorem, no (n−2)×180 polygon formula, no algebra, no bearings, no circle theorems.
Band A
Section A · Fluency
Single angle facts — straight line, point, vertically opposite. Clean numbers.
Q1.On a straight line, the angles 66° and x meet. Work out x.
66°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 66° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 66°. We do not know x.
  4. Take from 180. 180 − 66 = 114.
Answer: x = 114°
Q2.The angle x sits next to 30° on a straight line. Find x.
30°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 30° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 30°. We do not know x.
  4. Take from 180. 180 − 30 = 150.
Answer: x = 150°
Q3.A straight line is split into two angles, 88° and x. Find x.
88°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 88° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 88°. We do not know x.
  4. Take from 180. 180 − 88 = 92.
Answer: x = 92°
Q4.A triangle has angles 50°, 49° and x. Find x.
50°49°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 50° and 49°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 50 + 49 = 99.
  4. Take from 180. 180 − 99 = 81.
Answer: x = 81°
Q5.Two angles on a straight line are 60° and x. Find x.
60°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 60° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 60°. We do not know x.
  4. Take from 180. 180 − 60 = 120.
Answer: x = 120°
Q6.Angle x is the missing angle on a straight line that already has 114°. Find x.
114°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 114° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 114°. We do not know x.
  4. Take from 180. 180 − 114 = 66.
Answer: x = 66°
Q7.Three angles on a straight line are 73°, 46° and x. Find x.
x46°73°
°(1 mark)
  1. Read it. Three angles meet on one straight line: 73°, 46° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. Add the known angles. 73 + 46 = 119.
  4. Take from 180. 180 − 119 = 61.
Answer: x = 61°
Q8.On a straight line, the angles 79°, 46° and x meet at a point. Work out x.
79°x
°(1 mark)
  1. Read it. Two angles sit on a straight line: 79° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. The numbers. We know 79°. We do not know x.
  4. Take from 180. 180 − 79 = 101.
Answer: x = 55°
Q9.On a straight line, x is the third of three angles. The other two are 73° and 57°. Find x.
x57°73°
°(1 mark)
  1. Read it. Three angles meet on one straight line: 73°, 57° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. Add the known angles. 73 + 57 = 130.
  4. Take from 180. 180 − 130 = 50.
Answer: x = 50°
Q10.Three angles on a straight line are 66°, 34° and x. Find x.
x34°66°
°(1 mark)
  1. Read it. Three angles meet on one straight line: 66°, 34° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. Add the known angles. 66 + 34 = 100.
  4. Take from 180. 180 − 100 = 80.
Answer: x = 80°
Q11.On a straight line, x is the third of three angles. The other two are 76° and 68°. Find x.
x68°76°
°(1 mark)
  1. Read it. Three angles meet on one straight line: 76°, 68° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. Add the known angles. 76 + 68 = 144.
  4. Take from 180. 180 − 144 = 36.
Answer: x = 36°
Q12.A straight line is divided into three angles: 31°, 72° and x. Find x.
x72°31°
°(1 mark)
  1. Read it. Three angles meet on one straight line: 31°, 72° and x.
  2. The fact. Angles on a straight line add to 180°.
  3. Add the known angles. 31 + 72 = 103.
  4. Take from 180. 180 − 103 = 77.
Answer: x = 77°
Q13.Two straight lines cross. One angle is 108°. Find x, the angle vertically opposite.
108°x
°(1 mark)
  1. Read it. Two straight lines cross. One angle is 108°.
  2. The fact. When two lines cross, opposite angles are equal.
  3. Find the opposite one. x sits directly opposite the 108°.
  4. So they are the same. x is the same number as 108.
Answer: x = 108°
Q14.Two straight lines cross. One angle is 54°. Find x, the angle vertically opposite.
54°x
°(1 mark)
  1. Read it. Two straight lines cross. One angle is 54°.
  2. The fact. When two lines cross, opposite angles are equal.
  3. Find the opposite one. x sits directly opposite the 54°.
  4. So they are the same. x is the same number as 54.
Answer: x = 54°
Q15.Two lines cross at a point. A 117° angle sits in one corner. Find the angle x in the opposite corner.
117°x
°(1 mark)
  1. Read it. Two straight lines cross. One angle is 117°.
  2. The fact. When two lines cross, opposite angles are equal.
  3. Find the opposite one. x sits directly opposite the 117°.
  4. So they are the same. x is the same number as 117.
Answer: x = 117°
Q16.Two lines cross at a point. A 84° angle sits in one corner. Find the angle x in the opposite corner.
84°x
°(1 mark)
  1. Read it. Two straight lines cross. One angle is 84°.
  2. The fact. When two lines cross, opposite angles are equal.
  3. Find the opposite one. x sits directly opposite the 84°.
  4. So they are the same. x is the same number as 84.
Answer: x = 84°
Q17.Four angles meet at a point. Three of them are 60°, 95° and 119°. Find the fourth, x.
60°95°119°x
°(1 mark)
  1. Read it. Four angles meet at one point: 60°, 95°, 119° and x.
  2. The fact. Angles at a point add to 360°.
  3. Add the known angles. 60 + 95 + 119 = 274.
  4. Take from 360. 360 − 274 = 86.
Answer: x = 86°
Q18.At a single point, four angles fit together. Three are 92°, 90° and 97°. Find x, the last.
92°90°97°x
°(1 mark)
  1. Read it. Four angles meet at one point: 92°, 90°, 97° and x.
  2. The fact. Angles at a point add to 360°.
  3. Add the known angles. 92 + 90 + 97 = 279.
  4. Take from 360. 360 − 279 = 81.
Answer: x = 81°
Q19.Four angles meet at a point. Three of them are 111°, 118° and 58°. Find the fourth, x.
111°118°58°x
°(1 mark)
  1. Read it. Four angles meet at one point: 111°, 118°, 58° and x.
  2. The fact. Angles at a point add to 360°.
  3. Add the known angles. 111 + 118 + 58 = 287.
  4. Take from 360. 360 − 287 = 73.
Answer: x = 73°
Q20.At a point, the angles 100°, 87°, 45° and x fit around. Find x.
100°87°45°x
°(1 mark)
  1. Read it. Four angles meet at one point: 100°, 87°, 45° and x.
  2. The fact. Angles at a point add to 360°.
  3. Add the known angles. 100 + 87 + 45 = 232.
  4. Take from 360. 360 − 232 = 128.
Answer: x = 128°
Band B
Section B · Triangles & quadrilaterals
Including isosceles cases.
Q21.A triangle has angles 70°, 31° and x. Find x.
70°31°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 70° and 31°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 70 + 31 = 101.
  4. Take from 180. 180 − 101 = 79.
Answer: x = 79°
Q22.A triangle has angles 79°, 73° and x. Find x.
79°73°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 79° and 73°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 79 + 73 = 152.
  4. Take from 180. 180 − 152 = 28.
Answer: x = 28°
Q23.Two angles of a triangle are 54° and 43°. Find the third, x.
54°43°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 54° and 43°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 54 + 43 = 97.
  4. Take from 180. 180 − 97 = 83.
Answer: x = 83°
Q24.A triangle has angles 59°, 36° and x. Find x.
59°36°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 59° and 36°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 59 + 36 = 95.
  4. Take from 180. 180 − 95 = 85.
Answer: x = 85°
Q25.A triangle has interior angles of 45° and 48°. The third interior angle is x. Find x.
45°48°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 45° and 48°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 45 + 48 = 93.
  4. Take from 180. 180 − 93 = 87.
Answer: x = 87°
Q26.A triangle has angles 66°, 65° and x. Find x.
66°65°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 66° and 65°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 66 + 65 = 131.
  4. Take from 180. 180 − 131 = 49.
Answer: x = 49°
Q27.A right-angled triangle has another angle of 47°. Find the third angle, x.
90°47°x
°(1 mark)
  1. Read it. A right-angled triangle. One angle is the right angle (90°). Another is 47°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 90 + 47 = 137.
  4. Take from 180. 180 − 137 = 43.
Answer: x = 43°
Q28.A right-angled triangle has another angle of 28°. Find the third angle, x.
90°28°x
°(1 mark)
  1. Read it. A right-angled triangle. One angle is the right angle (90°). Another is 28°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 90 + 28 = 118.
  4. Take from 180. 180 − 118 = 62.
Answer: x = 62°
Q29.In a right-angled triangle, one of the other two angles is 67°. Find x, the remaining angle.
90°67°x
°(1 mark)
  1. Read it. A right-angled triangle. One angle is the right angle (90°). Another is 67°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 90 + 67 = 157.
  4. Take from 180. 180 − 157 = 23.
Answer: x = 23°
Q30.An isosceles triangle has base angles of 75°. Find the apex, x.
75°75°x
°(1 mark)
  1. Read it. An isosceles triangle. The two base angles are equal — each is 75°. The apex is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the two base angles. 75 + 75 = 150.
  4. Take from 180. 180 − 150 = 30.
Answer: x = 30°
Q31.In an isosceles triangle, the two equal base angles are each 47°. Find the angle at the apex, x.
°(1 mark)
  1. Read it. An isosceles triangle. The two base angles are equal — each is 47°. The apex is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the two base angles. 47 + 47 = 94.
  4. Take from 180. 180 − 94 = 86.
Answer: x = 86°
Q32.In an isosceles triangle, the two equal base angles are each 44°. Find the angle at the apex, x.
°(1 mark)
  1. Read it. An isosceles triangle. The two base angles are equal — each is 44°. The apex is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the two base angles. 44 + 44 = 88.
  4. Take from 180. 180 − 88 = 92.
Answer: x = 92°
Q33.An isosceles triangle has base angles of 64°. Find the apex, x.
°(1 mark)
  1. Read it. An isosceles triangle. The two base angles are equal — each is 64°. The apex is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the two base angles. 64 + 64 = 128.
  4. Take from 180. 180 − 128 = 52.
Answer: x = 52°
Q34.A triangle is isosceles with an apex of 76°. Find the size of either base angle, x.
°(1 mark)
  1. Read it. An isosceles triangle. The apex angle is 76°. The two base angles are equal, and each is x.
  2. The fact. The three angles in a triangle add to 180°. The two base angles are equal.
  3. Take the apex from 180. 180 − 76 = 104. (This is the total of the two base angles.)
  4. Share equally between the two. 104 ÷ 2 = 52.
Answer: x = 52°
Q35.An isosceles triangle has an apex angle of 74°. Find one of the equal base angles, x.
°(1 mark)
  1. Read it. An isosceles triangle. The apex angle is 74°. The two base angles are equal, and each is x.
  2. The fact. The three angles in a triangle add to 180°. The two base angles are equal.
  3. Take the apex from 180. 180 − 74 = 106. (This is the total of the two base angles.)
  4. Share equally between the two. 106 ÷ 2 = 53.
Answer: x = 53°
Q36.A triangle is isosceles with an apex of 88°. Find the size of either base angle, x.
°(1 mark)
  1. Read it. An isosceles triangle. The apex angle is 88°. The two base angles are equal, and each is x.
  2. The fact. The three angles in a triangle add to 180°. The two base angles are equal.
  3. Take the apex from 180. 180 − 88 = 92. (This is the total of the two base angles.)
  4. Share equally between the two. 92 ÷ 2 = 46.
Answer: x = 46°
Q37.A four-sided shape has angles 68°, 123°, 88° and x. Work out x.
°(1 mark)
  1. Read it. A four-sided shape. Three angles known: 68°, 123°, 88°. The fourth is x.
  2. The fact. The four angles in a four-sided shape add to 360°.
  3. Add the known angles. 68 + 123 + 88 = 279.
  4. Take from 360. 360 − 279 = 81.
Answer: x = 81°
Q38.In a quadrilateral, three of the interior angles are 113°, 128° and 77°. Find the fourth, x.
°(1 mark)
  1. Read it. A four-sided shape. Three angles known: 113°, 128°, 77°. The fourth is x.
  2. The fact. The four angles in a four-sided shape add to 360°.
  3. Add the known angles. 113 + 128 + 77 = 318.
  4. Take from 360. 360 − 318 = 42.
Answer: x = 42°
Q39.A quadrilateral has angles 120°, 102°, 67° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape. Three angles known: 120°, 102°, 67°. The fourth is x.
  2. The fact. The four angles in a four-sided shape add to 360°.
  3. Add the known angles. 120 + 102 + 67 = 289.
  4. Take from 360. 360 − 289 = 71.
Answer: x = 71°
Q40.In a quadrilateral, three of the interior angles are 123°, 69° and 120°. Find the fourth, x.
°(1 mark)
  1. Read it. A four-sided shape. Three angles known: 123°, 69°, 120°. The fourth is x.
  2. The fact. The four angles in a four-sided shape add to 360°.
  3. Add the known angles. 123 + 69 + 120 = 312.
  4. Take from 360. 360 − 312 = 48.
Answer: x = 48°
Band C
Section C · Two-step problems
Chain two facts together.
Q41.A triangle has one angle equal to (180° − 95°), and another angle of 33°. Find the third angle, x. (The 95° sits on a straight line next to the triangle.)
°(1 mark)
  1. Read it. A triangle. One angle equals (180° − 95°). Another angle is 33°. The third angle is x.
  2. Use the first fact. Angles on a straight line add to 180°. So one triangle angle is 180° − the angle on the line.
  3. Find that triangle angle. 180 − 95 = 85.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 85 + 33 = 118.
  6. Take from 180. 180 − 118 = 62.
Answer: x = 62°
Q42.A triangle has one angle equal to (180° − 123°), and another angle of 64°. Find the third angle, x. (The 123° sits on a straight line next to the triangle.)
°(1 mark)
  1. Read it. A triangle. One angle equals (180° − 123°). Another angle is 64°. The third angle is x.
  2. Use the first fact. Angles on a straight line add to 180°. So one triangle angle is 180° − the angle on the line.
  3. Find that triangle angle. 180 − 123 = 57.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 57 + 64 = 121.
  6. Take from 180. 180 − 121 = 59.
Answer: x = 59°
Q43.A triangle has one angle equal to (180° − 126°), and another angle of 41°. Find the third angle, x. (The 126° sits on a straight line next to the triangle.)
°(1 mark)
  1. Read it. A triangle. One angle equals (180° − 126°). Another angle is 41°. The third angle is x.
  2. Use the first fact. Angles on a straight line add to 180°. So one triangle angle is 180° − the angle on the line.
  3. Find that triangle angle. 180 − 126 = 54.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 54 + 41 = 95.
  6. Take from 180. 180 − 95 = 85.
Answer: x = 85°
Q44.A triangle has one angle equal to (180° − 116°), and another angle of 67°. Find the third angle, x. (The 116° sits on a straight line next to the triangle.)
°(1 mark)
  1. Read it. A triangle. One angle equals (180° − 116°). Another angle is 67°. The third angle is x.
  2. Use the first fact. Angles on a straight line add to 180°. So one triangle angle is 180° − the angle on the line.
  3. Find that triangle angle. 180 − 116 = 64.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 64 + 67 = 131.
  6. Take from 180. 180 − 131 = 49.
Answer: x = 49°
Q45.A triangle has one angle equal to (180° − 103°), and another angle of 49°. Find the third angle, x. (The 103° sits on a straight line next to the triangle.)
°(1 mark)
  1. Read it. A triangle. One angle equals (180° − 103°). Another angle is 49°. The third angle is x.
  2. Use the first fact. Angles on a straight line add to 180°. So one triangle angle is 180° − the angle on the line.
  3. Find that triangle angle. 180 − 103 = 77.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 77 + 49 = 126.
  6. Take from 180. 180 − 126 = 54.
Answer: x = 54°
Q46.Two lines cross to make a vertically opposite pair of 50°. That 50° is one angle of a triangle whose other angle is 47°. Find the third angle of the triangle, x.
°(1 mark)
  1. Read it. Two lines cross to make a vertically opposite pair of 50°. That same 50° is one angle of a triangle. Another triangle angle is 47°. Find the third triangle angle, x.
  2. Use the first fact. Vertically opposite angles are equal. So one triangle angle is 50°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 50 + 47 = 97.
  5. Take from 180. 180 − 97 = 83.
Answer: x = 83°
Q47.Two lines cross to make a vertically opposite pair of 75°. That 75° is one angle of a triangle whose other angle is 70°. Find the third angle of the triangle, x.
°(1 mark)
  1. Read it. Two lines cross to make a vertically opposite pair of 75°. That same 75° is one angle of a triangle. Another triangle angle is 70°. Find the third triangle angle, x.
  2. Use the first fact. Vertically opposite angles are equal. So one triangle angle is 75°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 75 + 70 = 145.
  5. Take from 180. 180 − 145 = 35.
Answer: x = 35°
Q48.Two lines cross to make a vertically opposite pair of 53°. That 53° is one angle of a triangle whose other angle is 76°. Find the third angle of the triangle, x.
°(1 mark)
  1. Read it. Two lines cross to make a vertically opposite pair of 53°. That same 53° is one angle of a triangle. Another triangle angle is 76°. Find the third triangle angle, x.
  2. Use the first fact. Vertically opposite angles are equal. So one triangle angle is 53°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 53 + 76 = 129.
  5. Take from 180. 180 − 129 = 51.
Answer: x = 51°
Q49.Two lines cross to make a vertically opposite pair of 78°. That 78° is one angle of a triangle whose other angle is 36°. Find the third angle of the triangle, x.
°(1 mark)
  1. Read it. Two lines cross to make a vertically opposite pair of 78°. That same 78° is one angle of a triangle. Another triangle angle is 36°. Find the third triangle angle, x.
  2. Use the first fact. Vertically opposite angles are equal. So one triangle angle is 78°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 78 + 36 = 114.
  5. Take from 180. 180 − 114 = 66.
Answer: x = 66°
Q50.Two lines cross to make a vertically opposite pair of 64°. That 64° is one angle of a triangle whose other angle is 73°. Find the third angle of the triangle, x.
°(1 mark)
  1. Read it. Two lines cross to make a vertically opposite pair of 64°. That same 64° is one angle of a triangle. Another triangle angle is 73°. Find the third triangle angle, x.
  2. Use the first fact. Vertically opposite angles are equal. So one triangle angle is 64°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 64 + 73 = 137.
  5. Take from 180. 180 − 137 = 43.
Answer: x = 43°
Q51.Four angles meet at a point: 109°, 127°, 65° and angle p. Find p first. Then p is one angle of a triangle whose other angle is 30°. Find x, the third angle of the triangle.
°(1 mark)
  1. Read it. Four angles meet at a point: 109°, 127°, 65° and an angle called p. Then p is one angle of a triangle whose other angle is 30°. Find the third triangle angle, x.
  2. Use the first fact. Angles at a point add to 360°.
  3. Add the three known. 109 + 127 + 65 = 301.
  4. Find p. 360 − 301 = 59. So p is 59°.
  5. Use the second fact. The three angles in a triangle add to 180°.
  6. Add the known triangle angles. 59 + 30 = 89.
  7. Take from 180. 180 − 89 = 91.
Answer: x = 91°
Q52.Four angles meet at a point: 126°, 48°, 84° and angle p. Find p first. Then p is one angle of a triangle whose other angle is 31°. Find x, the third angle of the triangle.
°(1 mark)
  1. Read it. Four angles meet at a point: 126°, 48°, 84° and an angle called p. Then p is one angle of a triangle whose other angle is 31°. Find the third triangle angle, x.
  2. Use the first fact. Angles at a point add to 360°.
  3. Add the three known. 126 + 48 + 84 = 258.
  4. Find p. 360 − 258 = 102. So p is 102°.
  5. Use the second fact. The three angles in a triangle add to 180°.
  6. Add the known triangle angles. 102 + 31 = 133.
  7. Take from 180. 180 − 133 = 47.
Answer: x = 47°
Q53.Four angles meet at a point: 62°, 69°, 120° and angle p. Find p first. Then p is one angle of a triangle whose other angle is 35°. Find x, the third angle of the triangle.
°(1 mark)
  1. Read it. Four angles meet at a point: 62°, 69°, 120° and an angle called p. Then p is one angle of a triangle whose other angle is 35°. Find the third triangle angle, x.
  2. Use the first fact. Angles at a point add to 360°.
  3. Add the three known. 62 + 69 + 120 = 251.
  4. Find p. 360 − 251 = 109. So p is 109°.
  5. Use the second fact. The three angles in a triangle add to 180°.
  6. Add the known triangle angles. 109 + 35 = 144.
  7. Take from 180. 180 − 144 = 36.
Answer: x = 36°
Q54.Four angles meet at a point: 96°, 43°, 133° and angle p. Find p first. Then p is one angle of a triangle whose other angle is 66°. Find x, the third angle of the triangle.
°(1 mark)
  1. Read it. Four angles meet at a point: 96°, 43°, 133° and an angle called p. Then p is one angle of a triangle whose other angle is 66°. Find the third triangle angle, x.
  2. Use the first fact. Angles at a point add to 360°.
  3. Add the three known. 96 + 43 + 133 = 272.
  4. Find p. 360 − 272 = 88. So p is 88°.
  5. Use the second fact. The three angles in a triangle add to 180°.
  6. Add the known triangle angles. 88 + 66 = 154.
  7. Take from 180. 180 − 154 = 26.
Answer: x = 26°
Q55.Four angles meet at a point: 131°, 118°, 70° and angle p. Find p first. Then p is one angle of a triangle whose other angle is 53°. Find x, the third angle of the triangle.
°(1 mark)
  1. Read it. Four angles meet at a point: 131°, 118°, 70° and an angle called p. Then p is one angle of a triangle whose other angle is 53°. Find the third triangle angle, x.
  2. Use the first fact. Angles at a point add to 360°.
  3. Add the three known. 131 + 118 + 70 = 319.
  4. Find p. 360 − 319 = 41. So p is 41°.
  5. Use the second fact. The three angles in a triangle add to 180°.
  6. Add the known triangle angles. 41 + 53 = 94.
  7. Take from 180. 180 − 94 = 86.
Answer: x = 86°
Q56.A quadrilateral has angles (180° − 124°), 94°, 100° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape has angles (180° − 124°), 94°, 100° and x. Find x.
  2. Use the first fact. Angles on a straight line add to 180°. So one angle is 180° − the angle on the line.
  3. Find that first angle. 180 − 124 = 56.
  4. Use the second fact. The four angles in a four-sided shape add to 360°.
  5. Add the three known angles. 56 + 94 + 100 = 250.
  6. Take from 360. 360 − 250 = 110.
Answer: x = 110°
Q57.A quadrilateral has angles (180° − 142°), 117°, 117° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape has angles (180° − 142°), 117°, 117° and x. Find x.
  2. Use the first fact. Angles on a straight line add to 180°. So one angle is 180° − the angle on the line.
  3. Find that first angle. 180 − 142 = 38.
  4. Use the second fact. The four angles in a four-sided shape add to 360°.
  5. Add the three known angles. 38 + 117 + 117 = 272.
  6. Take from 360. 360 − 272 = 88.
Answer: x = 88°
Q58.A quadrilateral has angles (180° − 147°), 75°, 101° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape has angles (180° − 147°), 75°, 101° and x. Find x.
  2. Use the first fact. Angles on a straight line add to 180°. So one angle is 180° − the angle on the line.
  3. Find that first angle. 180 − 147 = 33.
  4. Use the second fact. The four angles in a four-sided shape add to 360°.
  5. Add the three known angles. 33 + 75 + 101 = 209.
  6. Take from 360. 360 − 209 = 151.
Answer: x = 151°
Q59.A quadrilateral has angles (180° − 133°), 90°, 87° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape has angles (180° − 133°), 90°, 87° and x. Find x.
  2. Use the first fact. Angles on a straight line add to 180°. So one angle is 180° − the angle on the line.
  3. Find that first angle. 180 − 133 = 47.
  4. Use the second fact. The four angles in a four-sided shape add to 360°.
  5. Add the three known angles. 47 + 90 + 87 = 224.
  6. Take from 360. 360 − 224 = 136.
Answer: x = 136°
Q60.A quadrilateral has angles (180° − 130°), 75°, 103° and x. Find x.
°(1 mark)
  1. Read it. A four-sided shape has angles (180° − 130°), 75°, 103° and x. Find x.
  2. Use the first fact. Angles on a straight line add to 180°. So one angle is 180° − the angle on the line.
  3. Find that first angle. 180 − 130 = 50.
  4. Use the second fact. The four angles in a four-sided shape add to 360°.
  5. Add the three known angles. 50 + 75 + 103 = 228.
  6. Take from 360. 360 − 228 = 132.
Answer: x = 132°
Band D
Section D · Parallel lines
Corresponding, alternate and co-interior pairs.
Q61.On a pair of parallel lines, a transversal makes an angle of 52°. Find x, the corresponding angle on the other parallel line.
52°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 52°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 52.
Answer: x = 52°
Q62.A transversal crosses two parallel lines. One angle is 63°. Find x, its corresponding angle.
63°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 63°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 63.
Answer: x = 63°
Q63.A transversal crosses two parallel lines. One angle is 78°. Find x, its corresponding angle.
78°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 78°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 78.
Answer: x = 78°
Q64.A transversal crosses two parallel lines. One angle is 72°. Find x, its corresponding angle.
72°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 72°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 72.
Answer: x = 72°
Q65.Two parallel lines are crossed by a transversal. A 104° angle sits on one line. Its corresponding partner on the other line is x. Find x.
104°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 104°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 104.
Answer: x = 104°
Q66.Two parallel lines meet a transversal. An F-shape forms with 38° at the top. Find x, the corresponding angle at the bottom.
38°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 38°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 38.
Answer: x = 38°
Q67.Two parallel lines meet a transversal. An F-shape forms with 32° at the top. Find x, the corresponding angle at the bottom.
32°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 32°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 32.
Answer: x = 32°
Q68.A Z-shape forms when a transversal crosses two parallel lines. One arm of the Z is 24°; find x, the other arm.
24°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 24°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 24.
Answer: x = 24°
Q69.On a pair of parallel lines, the alternate angles include 152° and x. Find x.
152°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 152°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 152.
Answer: x = 152°
Q70.On a pair of parallel lines, the alternate angles include 112° and x. Find x.
112°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 112°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 112.
Answer: x = 112°
Q71.A Z-shape forms when a transversal crosses two parallel lines. One arm of the Z is 138°; find x, the other arm.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 138°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 138.
Answer: x = 138°
Q72.A Z-shape forms when a transversal crosses two parallel lines. One arm of the Z is 67°; find x, the other arm.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 67°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 67.
Answer: x = 67°
Q73.Two parallel lines are cut by a transversal. A 58° angle is given. Its alternate angle, on the other line, is x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 58°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 58.
Answer: x = 58°
Q74.Two parallel lines are cut by a transversal. A 146° angle is given. Its alternate angle, on the other line, is x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 146°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 146.
Answer: x = 146°
Q75.Two parallel lines and a transversal form a C-shape of co-interior angles, 44° and x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 44°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 44 = 136.
Answer: x = 136°
Q76.A transversal crosses two parallel lines. One co-interior angle is 132°. Find x, the other co-interior angle.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 132°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 132 = 48.
Answer: x = 48°
Q77.A transversal crosses two parallel lines. One co-interior angle is 118°. Find x, the other co-interior angle.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 118°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 118 = 62.
Answer: x = 62°
Q78.Two parallel lines and a transversal form a C-shape of co-interior angles, 98° and x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 98°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 98 = 82.
Answer: x = 82°
Q79.On a pair of parallel lines, two co-interior angles are 124° and x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 124°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 124 = 56.
Answer: x = 56°
Q80.Two parallel lines and a transversal form a C-shape of co-interior angles, 84° and x. Find x.
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 84°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 84 = 96.
Answer: x = 96°
Band E
Section E · Reasoning
State the rule. Multi-step. Hardest a Grade 3 pupil can meet.
Q81.Two parallel lines are crossed by a transversal. The alternate angle inside the triangle is 38°. The triangle also has another angle of 49°. Find the third angle, x. State the two rules you used.
38°x
°(1 mark)
  1. Read it. Two parallel lines. A transversal makes an alternate angle of 38° inside a triangle. The triangle has another angle of 49°. The third angle is x.
  2. Use the first fact. Alternate angles are equal. So one triangle angle is 38°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 38 + 49 = 87.
  5. Take from 180. 180 − 87 = 93.
Answer: x = 93°
Q82.Two parallel lines are crossed by a transversal. The alternate angle inside the triangle is 49°. The triangle also has another angle of 67°. Find the third angle, x. State the two rules you used.
49°x
°(1 mark)
  1. Read it. Two parallel lines. A transversal makes an alternate angle of 49° inside a triangle. The triangle has another angle of 67°. The third angle is x.
  2. Use the first fact. Alternate angles are equal. So one triangle angle is 49°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 49 + 67 = 116.
  5. Take from 180. 180 − 116 = 64.
Answer: x = 64°
Q83.Two parallel lines are crossed by a transversal. The alternate angle inside the triangle is 54°. The triangle also has another angle of 56°. Find the third angle, x. State the two rules you used.
54°x
°(1 mark)
  1. Read it. Two parallel lines. A transversal makes an alternate angle of 54° inside a triangle. The triangle has another angle of 56°. The third angle is x.
  2. Use the first fact. Alternate angles are equal. So one triangle angle is 54°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 54 + 56 = 110.
  5. Take from 180. 180 − 110 = 70.
Answer: x = 70°
Q84.Two parallel lines are crossed by a transversal. The alternate angle inside the triangle is 48°. The triangle also has another angle of 36°. Find the third angle, x. State the two rules you used.
48°x
°(1 mark)
  1. Read it. Two parallel lines. A transversal makes an alternate angle of 48° inside a triangle. The triangle has another angle of 36°. The third angle is x.
  2. Use the first fact. Alternate angles are equal. So one triangle angle is 48°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 48 + 36 = 84.
  5. Take from 180. 180 − 84 = 96.
Answer: x = 96°
Q85.Two parallel lines are crossed by a transversal. The alternate angle inside the triangle is 67°. The triangle also has another angle of 68°. Find the third angle, x. State the two rules you used.
67°x
°(1 mark)
  1. Read it. Two parallel lines. A transversal makes an alternate angle of 67° inside a triangle. The triangle has another angle of 68°. The third angle is x.
  2. Use the first fact. Alternate angles are equal. So one triangle angle is 67°.
  3. Use the second fact. The three angles in a triangle add to 180°.
  4. Add the known triangle angles. 67 + 68 = 135.
  5. Take from 180. 180 − 135 = 45.
Answer: x = 45°
Q86.An isosceles triangle has base angles of 53°. The apex sits on a straight line; the angle on the other side of the line, next to the apex, is x. Find x. Give the two rules used.
53°53°x
°(1 mark)
  1. Read it. An isosceles triangle has base angles of 53°. The apex sits on a straight line. x is the angle on the other side of the line, next to the apex.
  2. Use the first fact. Triangle angles add to 180°. The two base angles are equal.
  3. Find the apex. 180 − 53 − 53 = 74.
  4. Use the second fact. Angles on a straight line add to 180°.
  5. Take the apex from 180. 180 − 74 = 106.
Answer: x = 106°
Q87.An isosceles triangle has base angles of 64°. The apex sits on a straight line; the angle on the other side of the line, next to the apex, is x. Find x. Give the two rules used.
64°64°x
°(1 mark)
  1. Read it. An isosceles triangle has base angles of 64°. The apex sits on a straight line. x is the angle on the other side of the line, next to the apex.
  2. Use the first fact. Triangle angles add to 180°. The two base angles are equal.
  3. Find the apex. 180 − 64 − 64 = 52.
  4. Use the second fact. Angles on a straight line add to 180°.
  5. Take the apex from 180. 180 − 52 = 128.
Answer: x = 128°
Q88.An isosceles triangle has base angles of 57°. The apex sits on a straight line; the angle on the other side of the line, next to the apex, is x. Find x. Give the two rules used.
57°57°x
°(1 mark)
  1. Read it. An isosceles triangle has base angles of 57°. The apex sits on a straight line. x is the angle on the other side of the line, next to the apex.
  2. Use the first fact. Triangle angles add to 180°. The two base angles are equal.
  3. Find the apex. 180 − 57 − 57 = 66.
  4. Use the second fact. Angles on a straight line add to 180°.
  5. Take the apex from 180. 180 − 66 = 114.
Answer: x = 114°
Q89.An isosceles triangle has base angles of 50°. The apex sits on a straight line; the angle on the other side of the line, next to the apex, is x. Find x. Give the two rules used.
50°50°x
°(1 mark)
  1. Read it. An isosceles triangle has base angles of 50°. The apex sits on a straight line. x is the angle on the other side of the line, next to the apex.
  2. Use the first fact. Triangle angles add to 180°. The two base angles are equal.
  3. Find the apex. 180 − 50 − 50 = 80.
  4. Use the second fact. Angles on a straight line add to 180°.
  5. Take the apex from 180. 180 − 80 = 100.
Answer: x = 100°
Q90.A triangle has interior angles of 37° and 63°. The third interior angle is x. Find x.
37°63°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 37° and 63°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 37 + 63 = 100.
  4. Take from 180. 180 − 100 = 80.
Answer: x = 80°
Q91.On a diagram of two parallel lines crossed by a transversal, angle P is 132° and angle Q is its corresponding partner. Find Q. State the rule.
132°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 132°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 132.
Answer: x = 132°
Q92.On a diagram of two parallel lines crossed by a transversal, angle P is 63° and angle Q is its corresponding partner. Find Q. State the rule.
63°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 63°. We need the matching (corresponding) angle, x.
  2. Spot the shape. Corresponding angles make an F-shape.
  3. The fact. Corresponding angles are equal.
  4. So the answer is the same. x is the same number as 63.
Answer: x = 63°
Q93.On a diagram of two parallel lines crossed by a transversal, angle P is 42° and angle Q is its co-interior partner. Find Q. State the rule.
42°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 42°. We need the co-interior angle, x.
  2. Spot the shape. Co-interior angles make a C-shape.
  3. The fact. Co-interior angles ADD to 180° (they are NOT equal).
  4. Take the known from 180. 180 − 42 = 138.
Answer: x = 138°
Q94.On a diagram of two parallel lines crossed by a transversal, angle P is 84° and angle Q is its alternate partner. Find Q. State the rule.
84°x
°(1 mark)
  1. Read it. Two parallel lines crossed by another line. One angle is 84°. We need the alternate angle, x.
  2. Spot the shape. Alternate angles make a Z-shape.
  3. The fact. Alternate angles are equal.
  4. So the answer is the same. x is the same number as 84.
Answer: x = 84°
Q95.In a triangle, the angles measure 36°, 39° and x. Work out x.
36°39°x
°(1 mark)
  1. Read it. A triangle. Two angles known: 36° and 39°. The third is x.
  2. The fact. The three angles in a triangle add to 180°.
  3. Add the known angles. 36 + 39 = 75.
  4. Take from 180. 180 − 75 = 105.
Answer: x = 105°
Q96.A straight line meets a triangle. One angle on the line is 149°; the angle inside the triangle next to it is therefore (180° − 149°). The triangle has another angle of 37°. Find the third angle x of the triangle, then state the angle vertically opposite x.
31°149°37°x
°(1 mark)
  1. Read it. A triangle sits on a straight line. One angle on the line is 149°. The triangle has another angle of 37°. Find the third triangle angle, x.
  2. Use the first fact. Angles on a straight line add to 180°.
  3. Find the angle inside the triangle. 180 − 149 = 31. This is the triangle angle next to the line.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 31 + 37 = 68.
  6. Take from 180. 180 − 68 = 112.
Answer: x = 112°
Q97.A straight line meets a triangle. One angle on the line is 111°; the angle inside the triangle next to it is therefore (180° − 111°). The triangle has another angle of 56°. Find the third angle x of the triangle, then state the angle vertically opposite x.
69°111°56°x
°(1 mark)
  1. Read it. A triangle sits on a straight line. One angle on the line is 111°. The triangle has another angle of 56°. Find the third triangle angle, x.
  2. Use the first fact. Angles on a straight line add to 180°.
  3. Find the angle inside the triangle. 180 − 111 = 69. This is the triangle angle next to the line.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 69 + 56 = 125.
  6. Take from 180. 180 − 125 = 55.
Answer: x = 55°
Q98.A straight line meets a triangle. One angle on the line is 110°; the angle inside the triangle next to it is therefore (180° − 110°). The triangle has another angle of 36°. Find the third angle x of the triangle, then state the angle vertically opposite x.
70°110°36°x
°(1 mark)
  1. Read it. A triangle sits on a straight line. One angle on the line is 110°. The triangle has another angle of 36°. Find the third triangle angle, x.
  2. Use the first fact. Angles on a straight line add to 180°.
  3. Find the angle inside the triangle. 180 − 110 = 70. This is the triangle angle next to the line.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 70 + 36 = 106.
  6. Take from 180. 180 − 106 = 74.
Answer: x = 74°
Q99.A straight line meets a triangle. One angle on the line is 118°; the angle inside the triangle next to it is therefore (180° − 118°). The triangle has another angle of 37°. Find the third angle x of the triangle, then state the angle vertically opposite x.
62°118°37°x
°(1 mark)
  1. Read it. A triangle sits on a straight line. One angle on the line is 118°. The triangle has another angle of 37°. Find the third triangle angle, x.
  2. Use the first fact. Angles on a straight line add to 180°.
  3. Find the angle inside the triangle. 180 − 118 = 62. This is the triangle angle next to the line.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 62 + 37 = 99.
  6. Take from 180. 180 − 99 = 81.
Answer: x = 81°
Q100.A straight line meets a triangle. One angle on the line is 113°; the angle inside the triangle next to it is therefore (180° − 113°). The triangle has another angle of 45°. Find the third angle x of the triangle, then state the angle vertically opposite x.
67°113°45°x
°(1 mark)
  1. Read it. A triangle sits on a straight line. One angle on the line is 113°. The triangle has another angle of 45°. Find the third triangle angle, x.
  2. Use the first fact. Angles on a straight line add to 180°.
  3. Find the angle inside the triangle. 180 − 113 = 67. This is the triangle angle next to the line.
  4. Use the second fact. The three angles in a triangle add to 180°.
  5. Add the known triangle angles. 67 + 45 = 112.
  6. Take from 180. 180 − 112 = 68.
Answer: x = 68°
/ 100

Answer key & mark scheme

QAnswerRule usedWorking
Q1114°Angles on a straight line add to 180°180 − 66 = 114
Q2150°Angles on a straight line add to 180°180 − 30 = 150
Q392°Angles on a straight line add to 180°180 − 88 = 92
Q481°Angles in a triangle add to 180°180 − 50 − 49 = 81
Q5120°Angles on a straight line add to 180°180 − 60 = 120
Q666°Angles on a straight line add to 180°180 − 114 = 66
Q761°Angles on a straight line add to 180°180 − 73 − 46 = 61
Q855°Angles on a straight line add to 180°180 − 79 − 46 = 55
Q950°Angles on a straight line add to 180°180 − 73 − 57 = 50
Q1080°Angles on a straight line add to 180°180 − 66 − 34 = 80
Q1136°Angles on a straight line add to 180°180 − 76 − 68 = 36
Q1277°Angles on a straight line add to 180°180 − 31 − 72 = 77
Q13108°Vertically opposite angles are equalVertically opposite ⇒ x = 108
Q1454°Vertically opposite angles are equalVertically opposite ⇒ x = 54
Q15117°Vertically opposite angles are equalVertically opposite ⇒ x = 117
Q1684°Vertically opposite angles are equalVertically opposite ⇒ x = 84
Q1786°Angles at a point add to 360°360 − 60 − 95 − 119 = 86
Q1881°Angles at a point add to 360°360 − 92 − 90 − 97 = 81
Q1973°Angles at a point add to 360°360 − 111 − 118 − 58 = 73
Q20128°Angles at a point add to 360°360 − 100 − 87 − 45 = 128
Q2179°Angles in a triangle add to 180°180 − 70 − 31 = 79
Q2228°Angles in a triangle add to 180°180 − 79 − 73 = 28
Q2383°Angles in a triangle add to 180°180 − 54 − 43 = 83
Q2485°Angles in a triangle add to 180°180 − 59 − 36 = 85
Q2587°Angles in a triangle add to 180°180 − 45 − 48 = 87
Q2649°Angles in a triangle add to 180°180 − 66 − 65 = 49
Q2743°Angles in a triangle add to 180°180 − 90 − 47 = 43
Q2862°Angles in a triangle add to 180°180 − 90 − 28 = 62
Q2923°Angles in a triangle add to 180°180 − 90 − 67 = 23
Q3030°Triangle 180°; isosceles base angles are equal180 − 2 × 75 = 30
Q3186°Triangle 180°; isosceles base angles are equal180 − 2 × 47 = 86
Q3292°Triangle 180°; isosceles base angles are equal180 − 2 × 44 = 92
Q3352°Triangle 180°; isosceles base angles are equal180 − 2 × 64 = 52
Q3452°Triangle 180°; isosceles base angles are equal(180 − 76) ÷ 2 = 52
Q3553°Triangle 180°; isosceles base angles are equal(180 − 74) ÷ 2 = 53
Q3646°Triangle 180°; isosceles base angles are equal(180 − 88) ÷ 2 = 46
Q3781°Angles in a quadrilateral add to 360°360 − 68 − 123 − 88 = 81
Q3842°Angles in a quadrilateral add to 360°360 − 113 − 128 − 77 = 42
Q3971°Angles in a quadrilateral add to 360°360 − 120 − 102 − 67 = 71
Q4048°Angles in a quadrilateral add to 360°360 − 123 − 69 − 120 = 48
Q4162°Line 180° → Triangle 180°adj = 180 − 95 = 85; then 180 − 85 − 33 = 62
Q4259°Line 180° → Triangle 180°adj = 180 − 123 = 57; then 180 − 57 − 64 = 59
Q4385°Line 180° → Triangle 180°adj = 180 − 126 = 54; then 180 − 54 − 41 = 85
Q4449°Line 180° → Triangle 180°adj = 180 − 116 = 64; then 180 − 64 − 67 = 49
Q4554°Line 180° → Triangle 180°adj = 180 − 103 = 77; then 180 − 77 − 49 = 54
Q4683°Vertically opposite → Triangle 180°voa gives 50; 180 − 50 − 47 = 83
Q4735°Vertically opposite → Triangle 180°voa gives 75; 180 − 75 − 70 = 35
Q4851°Vertically opposite → Triangle 180°voa gives 53; 180 − 53 − 76 = 51
Q4966°Vertically opposite → Triangle 180°voa gives 78; 180 − 78 − 36 = 66
Q5043°Vertically opposite → Triangle 180°voa gives 64; 180 − 64 − 73 = 43
Q5191°Point 360° → Triangle 180°p = 360 − 109 − 127 − 65 = 59; then 180 − 59 − 30 = 91
Q5247°Point 360° → Triangle 180°p = 360 − 126 − 48 − 84 = 102; then 180 − 102 − 31 = 47
Q5336°Point 360° → Triangle 180°p = 360 − 62 − 69 − 120 = 109; then 180 − 109 − 35 = 36
Q5426°Point 360° → Triangle 180°p = 360 − 96 − 43 − 133 = 88; then 180 − 88 − 66 = 26
Q5586°Point 360° → Triangle 180°p = 360 − 131 − 118 − 70 = 41; then 180 − 41 − 53 = 86
Q56110°Line 180° → Quadrilateral 360°derived = 180 − 124 = 56; 360 − 56 − 94 − 100 = 110
Q5788°Line 180° → Quadrilateral 360°derived = 180 − 142 = 38; 360 − 38 − 117 − 117 = 88
Q58151°Line 180° → Quadrilateral 360°derived = 180 − 147 = 33; 360 − 33 − 75 − 101 = 151
Q59136°Line 180° → Quadrilateral 360°derived = 180 − 133 = 47; 360 − 47 − 90 − 87 = 136
Q60132°Line 180° → Quadrilateral 360°derived = 180 − 130 = 50; 360 − 50 − 75 − 103 = 132
Q6152°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 52
Q6263°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 63
Q6378°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 78
Q6472°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 72
Q65104°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 104
Q6638°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 38
Q6732°Corresponding angles are equal (F-shape)Corresponding angles are equal, so x = 32
Q6824°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 24
Q69152°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 152
Q70112°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 112
Q71138°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 138
Q7267°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 67
Q7358°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 58
Q74146°Alternate angles are equal (Z-shape)Alternate angles are equal, so x = 146
Q75136°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 44 = 136
Q7648°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 132 = 48
Q7762°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 118 = 62
Q7882°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 98 = 82
Q7956°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 124 = 56
Q8096°Co-interior angles add to 180° (C-shape)Co-interior: 180 − 84 = 96
Q8193°Alternate angles → Triangle 180°alternate ⇒ 38 in triangle; 180 − 38 − 49 = 93
Q8264°Alternate angles → Triangle 180°alternate ⇒ 49 in triangle; 180 − 49 − 67 = 64
Q8370°Alternate angles → Triangle 180°alternate ⇒ 54 in triangle; 180 − 54 − 56 = 70
Q8496°Alternate angles → Triangle 180°alternate ⇒ 48 in triangle; 180 − 48 − 36 = 96
Q8545°Alternate angles → Triangle 180°alternate ⇒ 67 in triangle; 180 − 67 − 68 = 45
Q86106°Isosceles + Line 180°apex = 180 − 2×53 = 74; on a line: 180 − 74 = 106
Q87128°Isosceles + Line 180°apex = 180 − 2×64 = 52; on a line: 180 − 52 = 128
Q88114°Isosceles + Line 180°apex = 180 − 2×57 = 66; on a line: 180 − 66 = 114
Q89100°Isosceles + Line 180°apex = 180 − 2×50 = 80; on a line: 180 − 80 = 100
Q9080°Angles in a triangle add to 180°180 − 37 − 63 = 80
Q91132°Parallel-lines rule (named in the question)corresponding ⇒ Q = 132
Q9263°Parallel-lines rule (named in the question)corresponding ⇒ Q = 63
Q93138°Parallel-lines rule (named in the question)co-interior ⇒ Q = 138
Q9484°Parallel-lines rule (named in the question)alternate ⇒ Q = 84
Q95105°Angles in a triangle add to 180°180 − 36 − 39 = 105
Q96112°Line 180° → Triangle 180° → Vertically oppositeadj = 180 − 149 = 31; third = 180 − 31 − 37 = 112; vertically opposite x is also 112
Q9755°Line 180° → Triangle 180° → Vertically oppositeadj = 180 − 111 = 69; third = 180 − 69 − 56 = 55; vertically opposite x is also 55
Q9874°Line 180° → Triangle 180° → Vertically oppositeadj = 180 − 110 = 70; third = 180 − 70 − 36 = 74; vertically opposite x is also 74
Q9981°Line 180° → Triangle 180° → Vertically oppositeadj = 180 − 118 = 62; third = 180 − 62 − 37 = 81; vertically opposite x is also 81
Q10068°Line 180° → Triangle 180° → Vertically oppositeadj = 180 − 113 = 67; third = 180 − 67 − 45 = 68; vertically opposite x is also 68
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