GCSE · Angles & polygons

Angles in parallel linesExam-style questions

Why corresponding angles are equal, why alternate angles are equal, and why co-interior angles add up to 180° — plus the exact naming examiners accept, and the add-a-parallel-line trick for awkward figures.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
The diagram shows two parallel lines and a straight line crossing them.Diagram NOT accurately drawn

Work out the value of $x$ . (3 marks)
Level 3 · 3 marksTry it
2
The line $AFB$ is parallel to the line $CHGD$ .

$EFG$ is a straight line.Show that triangle $FGH$ is isosceles.

Give a reason for each stage of your working.

(5 marks)
Level 3 · 5 marksTry it
3
The diagram shows quadrilateral $PQRS$ .The angles marked on the diagram are in degrees.

Show that $PQRS$ is a trapezium.

(4 marks)
Level 3 · 4 marksTry it
4
The diagram shows two parallel lines crossed by a straight line.Diagram NOT accurately drawn

(a) Work out the size of the angle marked $y$ . Give a reason for your answer.

(b) Write down the size of the angle marked $z$ . Give a reason for your answer.
Level 3 · 4 marksTry it
5
The diagram shows two parallel lines crossed by a straight line.Diagram NOT accurately drawn

(a) Write down the size of the angle marked $y$ . Give a reason for your answer.

(b) Work out the size of the angle marked $z$ . Give a reason for your answer.
Level 3 · 4 marksTry it