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WAEC Mathematics 2008 Question 25

Question 25

Circle Theorems

In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.

Diagram for this question
  1. A.25°
  2. B.65°
  3. C.115°
  4. D.130°
Show the answer and explanation

Answer: B (65°)

Explanation

The 65° is an exterior angle at Q, so the interior ∠PQR = 180° − 65° = 115°. Opposite angles of a cyclic quadrilateral add to 180°, so x = 180° − 115° = 65°.