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WAEC Mathematics 2009 Question 38

Question 38

Circle Theorems

In the diagram, angle 200° is subtended at the centre of the circle. Find the value of x.

Diagram for this question
  1. A.30°
  2. B.50°
  3. C.80°
  4. D.100°
Show the answer and explanation

Answer: B (50°)

Explanation

The angle at the top of the circle is half the non-reflex angle at the centre: ½(360° − 200°) = 80°. The radii make isosceles triangles, so this top angle equals 30° + x. Hence x = 50°.