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JAMB Mathematics 1985 Question 40

Question 40

Circle Theorems

In the figure above POQ is the diameter of the circle PQRS. If PSR = 145°, find x°

Diagram for this question
  1. A.25°
  2. B.35°
  3. C.45°
  4. D.55°
  5. E.25°.
Show the answer and explanation

Answer: D (55°)

Explanation

PQRS is cyclic, so <PQR = 180° − 145° = 35°. <PRQ = 90° (angle in a semicircle), so x = <QPR = 180° − 90° − 35° = 55°.