2018Q2(c)(i)Circles

NumericalEasy1 mark

2(c)

PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82°, calculate:

Figure for this question

∠QRS

Topic: Circle theorems

Previous-year question practice database

Answer

Exam answer

PQRS is cyclic.

Opposite angles of a cyclic quadrilateral are supplementary: ∠QPS + ∠QRS = 180°.

73° + ∠QRS = 180° ∠QRS = 107°.

Answer: 107°.

Explanation

∠QPS and ∠QRS are opposite angles of cyclic quadrilateral PQRS.

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