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GCE Mathematics 1989 Question 31

Question 31

Circle Theorems

In the diagram below, O is the centre of the circle. If ∠PAQ = 75°, what is the value of ∠PBQ?

Diagram for this question
  1. A.15°
  2. B.75°
  3. C.105°
  4. D.150°
  5. E.210°
Show the answer and explanation

Answer: C (105°)

Explanation

APBQ is a cyclic quadrilateral, so opposite angles add up to 180°: ∠PBQ = 180° − 75° = 105°.