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GCE Mathematics 1990 Question 35

Question 35

Circle Theorems

In the diagram below, PQRS is a cyclic quadrilateral, ∠PSR = 86° and ∠QPR = 38°. Calculate ∠PRQ.

Diagram for this question
  1. A.58°
  2. B.53°
  3. C.48°
  4. D.43°
  5. E.38°
Show the answer and explanation

Answer: C (48°)

Explanation

Opposite angles of a cyclic quadrilateral add to 180°, so ∠PQR = 94°. In triangle PQR, ∠PRQ = 180° − 94° − 38° = 48°.