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WAEC Mathematics 2002 Question 45

Question 45

Circle Theorems

In the diagram, O is the centre of the circle, ∠SOR = 64° and ∠PSO = 36°. Calculate ∠PQR.

Diagram for this question
  1. A.100°
  2. B.96°
  3. C.94°
  4. D.86°
Show the answer and explanation

Answer: D (86°)

Explanation

OS = OR, so ∠OSR = (180 − 64)/2 = 58° and ∠PSR = 36 + 58 = 94°. Opposite angles of cyclic quadrilateral PQRS add to 180°, so ∠PQR = 86°.