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
$PQ$ and $RS$ are parallel straight lines. $A$ is a point on $PQ$ , and $B$ and $C$ are points on $RS$ with $AB = AC$ .

Angle $PAB = 48°$ .Diagram NOT accurately drawn

Work out the size of angle $BAC$ . You must give reasons for each stage of your working.
Level 4 · 4 marksTry it
2
The diagram shows two parallel lines crossed by a straight line.Diagram NOT accurately drawn

(a) Work out the value of $x$ .

(b) Work out the size of the smaller of the two marked angles.
Level 4 · 4 marksTry it
3
The diagram shows two parallel lines crossed by a straight line.Diagram NOT accurately drawn

Work out the value of $x$ . Give a reason for your answer.
Level 4 · 3 marksTry it
4
$APB$ and $QR$ are parallel straight lines. $P$ is joined to $Q$ and to $R$ .

Angle $PQR = 68°$ . Angle $QPR = 47°$ .Diagram NOT accurately drawn

Work out the size of angle $RPB$ . Give a reason for each stage of your working.
Level 4 · 4 marksTry it