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Angles in parallel lines practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of angles in parallel lines questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Two parallel lines are cut by a transversal. Angle x and an angle of 128° are corresponding angles. Work out the size of angle x.

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Answer: 128

  1. The given angle is 128°.
  2. Corresponding angles between parallel lines are equal, so x = 128°.
  • Method (1): The given angle is 128°.
  • Accuracy (1): Answer 128

Question 2 Easy

Two parallel lines are cut by a transversal. Angle x and an angle of 120° are alternate angles. Work out the size of angle x.

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Answer: 120

  1. The given angle is 120°.
  2. Alternate angles between parallel lines are equal, so x = 120°.
  • Method (1): The given angle is 120°.
  • Accuracy (1): Answer 120

Question 3 Medium

Two straight lines cross. One of the four angles is 92°. Work out the size of the angle directly opposite it.

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Answer: 92

  1. The given angle is 92°.
  2. Vertically opposite angles are equal, so the opposite angle is 92°.
  • Method (1): The given angle is 92°.
  • Accuracy (1): Answer 92

Question 4 Medium

Two parallel lines are cut by a transversal. Angle x and an angle of 32° are corresponding angles. Work out the size of angle x.

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Answer: 32

  1. The given angle is 32°.
  2. Corresponding angles between parallel lines are equal, so x = 32°.
  • Method (1): The given angle is 32°.
  • Accuracy (1): Answer 32

Question 5 Hard

Two parallel lines are cut by a transversal. Angle p is 78°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.

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Answer: 102

  1. Angles on a straight line add to 180°, so q = 180° − 78°.
  2. q = 102°.
  • Method (1): Angles on a straight line add to 180°, so q = 180° − 78°.
  • Accuracy (1): Answer 102

Question 6 Hard

Two straight lines cross. One of the four angles is 131°. Work out the size of the angle directly opposite it.

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Answer: 131

  1. The given angle is 131°.
  2. Vertically opposite angles are equal, so the opposite angle is 131°.
  • Method (1): The given angle is 131°.
  • Accuracy (1): Answer 131

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 11 marks

Two parallel lines are cut by a transversal. Angle x and an angle of 80° are alternate angles. Work out the size of angle x.

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Answer: 80

  1. The given angle is 80°.
  2. Alternate angles between parallel lines are equal, so x = 80°.
  3. Angle x = 80°.
  • Accuracy (1): Answer 80

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Two parallel lines are cut by a transversal. Angle x and an angle of 133° are corresponding angles. Work out the size of angle x.

  1. 133
  2. 47
  3. 227
Show answer

133 The result is 133.

Check 2

Two parallel lines are cut by a transversal. Angle x and an angle of 132° are alternate angles. Work out the size of angle x.

  1. 132
  2. 48
  3. 228
Show answer

132 The result is 132.

Check 3

Two parallel lines are cut by a transversal. Angle x and an angle of 35° are co-interior angles. Work out the size of angle x.

  1. 145
  2. 35
  3. 325
Show answer

145 The result is 145.

Check 4

Two parallel lines are cut by a transversal. Angle p is 105°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.

  1. 75
  2. 105
  3. 255
Show answer

75 The result is 75.

Check 5

Two straight lines cross. One of the four angles is 142°. Work out the size of the angle directly opposite it.

  1. 142
  2. 38
  3. 218
Show answer

142 The result is 142.

Check 6

Two parallel lines are cut by a transversal. Angle x and an angle of 57° are corresponding angles. Work out the size of angle x.

  1. 57
  2. 123
  3. 303
Show answer

57 The result is 57.

Check 7

Two parallel lines are cut by a transversal. Angle x and an angle of 121° are alternate angles. Work out the size of angle x.

  1. 121
  2. 59
  3. 239
Show answer

121 The result is 121.

Check 8

Two parallel lines are cut by a transversal. Angle x and an angle of 48° are co-interior angles. Work out the size of angle x.

  1. 132
  2. 48
  3. 312
Show answer

132 The result is 132.

Check 9

Two parallel lines are cut by a transversal. Angle p is 139°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.

  1. 41
  2. 139
  3. 221
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41 The result is 41.

Check 10

Two straight lines cross. One of the four angles is 51°. Work out the size of the angle directly opposite it.

  1. 51
  2. 129
  3. 309
Show answer

51 The result is 51.

Check 11

Two parallel lines are cut by a transversal. Angle x and an angle of 71° are corresponding angles. Work out the size of angle x.

  1. 71
  2. 109
  3. 289
Show answer

71 The result is 71.

Check 12

Two parallel lines are cut by a transversal. Angle x and an angle of 97° are alternate angles. Work out the size of angle x.

  1. 97
  2. 83
  3. 263
Show answer

97 The result is 97.

Check 13

Two parallel lines are cut by a transversal. Angle x and an angle of 74° are co-interior angles. Work out the size of angle x.

  1. 106
  2. 74
  3. 286
Show answer

106 The result is 106.

Check 14

Two parallel lines are cut by a transversal. Angle p is 78°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.

  1. 102
  2. 78
  3. 282
Show answer

102 The result is 102.

Check 15

Two straight lines cross. One of the four angles is 98°. Work out the size of the angle directly opposite it.

  1. 98
  2. 82
  3. 262
Show answer

98 The result is 98.

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