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JAMB Mathematics 1988 Question 30

Question 30

Circle Theorems

In the figure above, PQRS is a circle. If chords QR and RS are equal, calculate the value of x

Diagram for this question
  1. A.80°
  2. B.60°
  3. C.45°
  4. D.40°
Show the answer and explanation

Answer: D (40°)

Explanation

Angle QRS = 180° − 120° = 60°, and since QR = RS, triangle QRS is equilateral, so angle QSR = angle QPR = 60°. Angle PSR = 180° − 100° = 80° and angle QPS = 180° − 60° = 120°, so angle SPR = 60°. In triangle PSR, x = 180° − 80° − 60° = 40°.