GCSE Mathematics › M4.1 Properties of shapes and angles

Properties of shapes and angles

Free GCSE Mathematics practice questions on Properties of shapes and angles. Aligned with the UK Department for Education GCSE subject content — works for any UK GCSE exam board. Sample questions below with detailed mark schemes. Sign up to practise the full set with spaced repetition.

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Explain — 2 marks

A gardener is designing a flower bed in the shape of a quadrilateral. The diagram shows the flower bed ABCD with angle ABC marked as 110° and side AB parallel to side CD.

(a) Explain why angle BCD must be 70°. [1 mark]
(b) Given that angle BAD is 75°, explain why angle ADC must be 105°. [1 mark]

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(a) Co-interior/allied angles add up to 180° (or angles on a straight line/add to 180° if using alternate approach)
(a) 180° − 110° = 70°
(b) Angles in a quadrilateral add up to 360°
(b) 360° − 110° − 70° − 75° = 105° (or equivalent method showing correct working)

Describe — 3 marks

The diagram shows a regular pentagon ABCDE with diagonals AC and AD drawn from vertex A.

(a) Describe the type of triangle formed by triangle ABC. [1 mark]
(b) Describe how to calculate the size of angle ABC. You must show your working. [2 marks]

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(a) Isosceles (triangle)
(b) Method: (5-2) × 180 ÷ 5 or 540 ÷ 5 or equivalent method to find interior angle
(b) 108°

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M4.2 Pythagoras and trigonometry

Properties of shapes and angles

Explain — 2 marks

Describe — 3 marks

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