GCSE · Angles & polygons

Angle rules & giving reasonsExam-style questions

Why angles at a point make 360°, angles on a straight line make 180°, and vertically opposite angles are equal; the triangle and quadrilateral angle sums; isosceles triangles; and how to write the reasons examiners insist on.

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$ABC$ is a triangle with $AB = AC$ . $BCD$ is a straight line.

Angle $BAC = 44°$ .Diagram NOT accurately drawn

Work out the size of the angle marked $x$ . You must give reasons for each stage of your working.
Level 3 · 5 marksTry it
2
The diagram shows a triangle.Diagram NOT accurately drawn

Work out the size of the largest angle of the triangle.
Level 3 · 3 marksTry it
3
The diagram shows four angles meeting at a point.Diagram NOT accurately drawn

Work out the size of the angle marked $2x°$ .
Level 3 · 3 marksTry it
4
Triangle $PQR$ has $PQ = PR$ .

Angle $PQR = 65°$ .Diagram NOT accurately drawn

Work out the size of angle $QPR$ . Give a reason for each stage of your working.
Level 3 · 3 marksTry it
5
The diagram shows two straight lines crossing at a point.Diagram NOT accurately drawn

Work out the value of $x$ . Give a reason for your answer.
Level 3 · 3 marksTry it