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JAMB Mathematics 1994 Question 27

Question 27

Circle Theorems

In the diagram above O is the centre of the circle. If SOQ is a diameter and ∠PRS is 38°, what is the value of ∠PSQ?

Diagram for this question
  1. A.148°
  2. B.104°
  3. C.80°
  4. D.52°
Show the answer and explanation

Answer: D (52°)

Explanation

Angle PQS = angle PRS = 38° (same segment). Angle SPQ = 90° (angle in a semicircle). So angle PSQ = 180° − 90° − 38° = 52°.