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WAEC Mathematics 2021 Question 37

Question 37

Circle Theorems

In the diagram, PQRS is a circle. Find the value of x.

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

Answer: A (50°)

Explanation

Opposite angles of a cyclic quadrilateral add to 180°: x + (x + y) = 180° and x + (2y − 30°) = 180°. So 2x + y = 180 and x + 2y = 210, giving x = 50°.