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WAEC Mathematics 2004 Question 33

Question 33

Circle Theorems

In the diagram, PQRW is a circle. Line PW and QR are produced to meet at M, where ∠WMR = 30° and |WM| = |MR|. Find the value of x

Diagram for this question
  1. A.10°
  2. B.25°
  3. C.35°
  4. D.60°
Show the answer and explanation

Answer: B (25°)

Explanation

WM = MR, so ∠MRW = (180 − 30)/2 = 75°. The exterior angle of cyclic quadrilateral PQRW at R equals the opposite interior angle at P: 3x = 75°, x = 25°.