Find angles made by a line crossing parallel lines, and give the exact reason (alternate, corresponding, co-interior) each time. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A transversal cutting a pair of parallel lines makes three famous pairs: alternate angles (Z, equal), corresponding angles (F, equal), co-interior angles (C or U, add to 180∘). Vertically opposite angles and straight-line facts still apply. The mark scheme wants the proper reason-word, not just a number.
Work through a diagram one angle at a time, writing a reason next to each. If angles are expressions in x, the same facts become an equation. Do not use 'parallel angles' or 'Z angles' as the written reason — write 'alternate angles' or 'corresponding angles' with 'parallel lines' if the board wording needs it.
A transversal makes F (corresponding, equal), Z (alternate, equal) and C (co-interior, add to 180∘). Write the reason next to the size — a bare 54∘ with no reason loses the second mark.
Objectives
They sit in the same position at each intersection. They are equal.
They sit on opposite sides of the transversal, between the parallel lines. They are equal.
They sit on the same side of the transversal, between the parallel lines.
Key points
Recognise alternate angles (Z shape), corresponding angles (F shape) and co-interior angles (C or U shape).
Use vertically opposite angles and angles on a straight line alongside the parallel-line facts.
Write a reason in the accepted wording every time you find an angle.
Form and solve an equation when angles are given as expressions in x.
Worked examples
Example 1
Two parallel lines are cut by a transversal. Angle x and an angle of 51° are corresponding angles. Work out the size of angle x.
1 marks
The given angle is 51°.
Corresponding angles between parallel lines are equal, so x = 51°.
Angle x = 51°.
Answer: 51
Common slips
Slip: The given angle is 53°. That changes a number from the question, so it answers a different question.
Slip: Corresponding angles between parallel lines are equal, so x = 54°. That changes a number in the working, so the step no longer follows from the one before.
Slip: Angle x = 55°. That does not match the working above it.
Example 2
Two parallel lines are cut by a transversal. Angle x and an angle of 118° are co-interior angles. Work out the size of angle x.
2 marks
Co-interior angles between parallel lines add to 180°.
x = 180° − 118°.
Angle x = 62°.
Answer: 62
Common slips
Slip: Co-interior angles between parallel lines add to 182°. That changes a number from the question, so it answers a different question.
Slip: x = 183° − 118°. That changes a number in the working, so the step no longer follows from the one before.
Slip: Angle x = 66°. That does not match the working above it.
Example 3
Two parallel lines are cut by a transversal. Angle p is 97°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.
2 marks
Angles on a straight line add to 180°, so q = 180° − 97°.
q = 83°.
Corresponding angles are equal, so r = 83°.
Answer: 83
Common slips
Slip: Angles on a straight line add to 182°, so q = 180° − 97°. That changes a number from the question, so it answers a different question.
Slip: q = 86°. That changes a number in the working, so the step no longer follows from the one before.
Slip: Corresponding angles are equal, so r = 87°. That does not match the working above it.
Questions and answers
GCSE Maths angles in parallel lines questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Two parallel lines are cut by a transversal. Angle p is 84°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.
Show answer
Answer: 96
Angles on a straight line add to 180°, so q = 180° − 84°.
q = 96°.
M1 — Angles on a straight line add to 180°, so q = 180° − 84°.
A1 — Answer 96
Question 2 Easy2 marks
Two straight lines cross. One of the four angles is 62°. Work out the size of the angle directly opposite it.
Show answer
Answer: 62
The given angle is 62°.
Vertically opposite angles are equal, so the opposite angle is 62°.
M1 — The given angle is 62°.
A1 — Answer 62
Question 3 Medium2 marks
Two parallel lines are cut by a transversal. Angle x and an angle of 91° are co-interior angles. Work out the size of angle x.
Show answer
Answer: 89
Co-interior angles between parallel lines add to 180°.
x = 180° − 91°.
M1 — Co-interior angles between parallel lines add to 180°.
A1 — Answer 89
Question 4 Medium2 marks
Two parallel lines are cut by a transversal. Angle p is 92°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.
Show answer
Answer: 88
Angles on a straight line add to 180°, so q = 180° − 92°.
q = 88°.
M1 — Angles on a straight line add to 180°, so q = 180° − 92°.
A1 — Answer 88
Question 5 Hard2 marks
Two parallel lines are cut by a transversal. Angle x and an angle of 101° are alternate angles. Work out the size of angle x.
Show answer
Answer: 101
The given angle is 101°.
Alternate angles between parallel lines are equal, so x = 101°.
M1 — The given angle is 101°.
A1 — Answer 101
Question 6 Hard2 marks
Two parallel lines are cut by a transversal. Angle x and an angle of 103° are co-interior angles. Work out the size of angle x.
Show answer
Answer: 77
Co-interior angles between parallel lines add to 180°.
x = 180° − 103°.
M1 — Co-interior angles between parallel lines add to 180°.
A1 — Answer 77
Question 7 Exam-style2 marks
Two parallel lines are cut by a transversal. Angle p is 70°. Angle q is on a straight line with angle p. Angle r is corresponding to angle q. Work out the size of angle r.
Show answer
Answer: 110
Angles on a straight line add to 180°, so q = 180° − 70°.
q = 110°.
Corresponding angles are equal, so r = 110°.
M1 — Angles on a straight line add to 180°, so q = 180° − 70°.
A1 — Answer 110
Common mistakes
Most lost marks on this topic are one slip.
Treating co-interior angles as equal.
They add to 180°.
Using an alternate-angle reason when the angles are corresponding.
Name the pair you actually used.
Applying the rule when the lines are not parallel.
The question has to give parallel lines, or you have to know they are parallel.
Spot the slip
Co-interior angles add to
180°
90°
360°
Show the slip
180° They sit between the parallel lines on the same side of the transversal.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Reasons are marked separately: a correct angle with no reason often scores only half the marks.
Write one reason per line of working, matched to the step that used it.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.