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WAEC Mathematics 2026 Question 44

Question 44

Circle Theorems

In the diagram, P, Q and R are points on a circle with centre O. ∠OPQ = 77° and ∠PQR = 130°. Find ∠ORQ

Diagram for this question
  1. A.90°
  2. B.57°
  3. C.33°
  4. D.53°
Show the answer and explanation

Answer: D (53°)

Explanation

∠PQR stands on the major arc PR, so the reflex angle POR = 260° and the angle POR inside OPQR is 100°. The angles of OPQR add to 360°: ∠ORQ = 360° − (77° + 130° + 100°) = 53°.