NumericalModerate1.5 marks
2(c)
PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82°, calculate:
∠RQS
Topic: Circle theorems
Previous-year question practice database
Answer
Exam answer
In ΔPQS: ∠PSQ = 180° − 73° − 55° = 52°.
Given ∠PSR = 82°: ∠QSR = 82° − 52° = 30°.
From part (i): ∠QRS = 107°.
In ΔQRS: ∠RQS = 180° − 107° − 30° = 43°.
Answer: 43°.
Explanation
First find ∠PSQ in triangle PQS, then split ∠PSR and use the angle sum of triangle QRS.