GCSE Mathematics › M4.1 Properties of shapes and angles

Properties of shapes and angles

Free AQA GCSE Mathematics practice questions on Properties of shapes and angles. 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.

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

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(01.1) Co-interior/allied angles add up to 180° (or angles on a straight line/add to 180° if using alternate approach)
(01.1) 180° − 110° = 70°
(01.2) Angles in a quadrilateral add up to 360°
(01.2) 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.

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

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(01.1) Isosceles (triangle)
(01.2) Method: (5-2) × 180 ÷ 5 or 540 ÷ 5 or equivalent method to find interior angle
(01.2) 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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