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WAEC Mathematics 2015 Question 19

Question 19

Circle Theorems

In the diagram, O is the centre of the circle, RT is a diameter, ∠PQT = 33° and ∠TOS = 76°. Calculate the value of angle PTR.

Diagram for this question
  1. A.73°
  2. B.67°
  3. C.57°
  4. D.37°
Show the answer and explanation

Answer: C (57°)

Explanation

∠TPR = 90° (angle in a semicircle) and ∠PRT = ∠PQT = 33° (same segment), so ∠PTR = 180° − 90° − 33° = 57°.