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WAEC Mathematics 2006 Question 21

Question 21

Circle Theorems

In the diagram P, Q, R, S are points on the circle, RQ̂S = 30°, PR̂S = 50° and PŜQ = 20°. What is the value of x° + y°?

Diagram for this question
  1. A.260°
  2. B.130°
  3. C.100°
  4. D.80°
Show the answer and explanation

Answer: B (130°)

Explanation

Angles in the same segment: y = ∠PQS = ∠PRS = 50° and ∠SPR = ∠SQR = 30°. In triangle PSR, ∠PSR = 180° − 50° − 30° = 100°, so x = 100° − 20° = 80°. x + y = 130°.