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WAEC Mathematics 1992 Question 23

Question 23

Circle Theorems

In the diagram below, O is the centre of the circle. QOR is a diameter and ∠PSR is 37°. Find ∠PRQ.

Diagram for this question
  1. A.37°
  2. B.53°
  3. C.65°
  4. D.127°
  5. E.147°
Show the answer and explanation

Answer: B (53°)

Explanation

∠PQR = ∠PSR = 37° (angles in the same segment) and ∠QPR = 90° (angle in a semicircle). So ∠PRQ = 180° − 90° − 37° = 53°.