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WAEC Mathematics 2025 Question 40

Question 40

Circle Theorems

In the diagram, P, Q, R and S are points on the circle with centre O. ∠QRS = (5x)° and ∠QOS = (6x + 24)°. Find ∠QPS.

Diagram for this question
  1. A.75°
  2. B.87°
  3. C.105°
  4. D.150°
Show the answer and explanation

Answer: A (75°)

Explanation

∠QPS = ½∠QOS = 3x + 12, and opposite angles of the cyclic quadrilateral give 5x + 3x + 12 = 180, so x = 21. ∠QPS = 3(21) + 12 = 75°.