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WAEC Mathematics 2013 Question 23

Question 23

Circle Theorems

In the diagram, O is the centre of the circle, OM||XZ and ∠ZOM = 25°. Calculate ∠XYZ.

Diagram for this question
  1. A.50°
  2. B.55°
  3. C.60°
  4. D.65°
Show the answer and explanation

Answer: D (65°)

Explanation

OM ∥ XZ gives ∠OZX = ∠ZOM = 25°. OX = OZ, so ∠OXZ = 25° and ∠XOZ = 130°. The angle at the circumference is half: ∠XYZ = 65°.