GCSE MATHS PRACTICE

GCSE Angles in Parallel Lines Questions

When a transversal crosses two parallel lines, corresponding angles are equal, alternate angles are equal and co-interior angles sum to 180°. Identify the positions of the angles before choosing a fact. You may also need angles on a straight line or vertically opposite angles. Matching arrow marks identify parallel lines. Use the given values rather than measuring the diagrams.

Updated 10 October 2026

Worked example

The marked lines are parallel. Find x and state the angle fact used.

Matching arrows mark parallel lines.

The 64° angle and x are in matching positions: both lie above a parallel line and to the right of the transversal.
They are corresponding angles. Corresponding angles on parallel lines are equal, so x = 64°.

Answer: x = 64° (corresponding angles)

Practice questions

1
Find x. The arrow-marked lines are parallel.
Matching arrows mark parallel lines.
Enlarged diagram
100%Scroll to inspect when enlarged.
2
Find x. The arrow-marked lines are parallel.
Matching arrows mark parallel lines.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
Find x. The arrow-marked lines are parallel.
Matching arrows mark parallel lines.
Enlarged diagram
100%Scroll to inspect when enlarged.
4
Find both x and y. The arrow-marked lines are parallel.
Matching arrows mark parallel lines.
Enlarged diagram
100%Scroll to inspect when enlarged.

Show answers

1. x = 118°
2. x = 71°
3. x = 68°
4. x = 56°, y = 124°

Common mistakes

Assuming any two angles are equal — Check their positions and whether the lines are marked parallel.
Making co-interior angles equal — Co-interior angles add to 180°; they are not generally equal.
Measuring the picture — Work from the given values and angle facts, not the apparent size of the drawing.

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GCSE Angles in Parallel Lines Questions

Updated 10 October 2026

Worked example

The marked lines are parallel. Find x and state the angle fact used.

Matching arrows mark parallel lines.

The 64° angle and x are in matching positions: both lie above a parallel line and to the right of the transversal.

They are corresponding angles. Corresponding angles on parallel lines are equal, so x = 64°.

Answer: x = 64° (corresponding angles)

Practice questions

Find x. The arrow-marked lines are parallel.

Matching arrows mark parallel lines.

Find x. The arrow-marked lines are parallel.

Matching arrows mark parallel lines.

Find x. The arrow-marked lines are parallel.

Matching arrows mark parallel lines.

Find both x and y. The arrow-marked lines are parallel.

Matching arrows mark parallel lines.

Show answers

1. x = 118°
2. x = 71°
3. x = 68°
4. x = 56°, y = 124°

Common mistakes

Assuming any two angles are equal — Check their positions and whether the lines are marked parallel.

Making co-interior angles equal — Co-interior angles add to 180°; they are not generally equal.

Measuring the picture — Work from the given values and angle facts, not the apparent size of the drawing.

GCSE Angles in Parallel Lines Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Angles in Parallel Lines Questions

Worked example

Practice questions

Common mistakes

Related resources