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. $X$ lies on the upper line, $Z$ lies on the lower line, and $M$ is a point between the lines.Diagram NOT accurately drawn

Work out the size of the angle marked $x$ . You must give reasons for each stage of your working.
Level 5 · 4 marksTry it
2
The diagram shows two parallel lines. $X$ lies on the upper line, $Z$ lies on the lower line, and $M$ is a point between the lines.

Angle $XMZ = 81°$ .Diagram NOT accurately drawn

Work out the value of $x$ . Show your working clearly, giving reasons.
Level 5 · 4 marksTry it