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WAEC Mathematics 2004 Question 13

Question 13

Circle Theorems

In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS

Diagram for this question
  1. A.35°
  2. B.70°
  3. C.100°
  4. D.125°
Show the answer and explanation

Answer: D (125°)

Explanation

∠PSQ = 90° (angle in a semicircle) and ∠SQP = 35°, so ∠SPQ = 55°. PQRS is cyclic, so ∠QRS = 180 − 55 = 125°.