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WAEC Mathematics 2019 Question 41

Question 41

Circle Theorems

In the diagram, RT is a tangent to the circle at R, ∠PQR = 70°, ∠QRT = 52°, ∠QSR = y and ∠PRQ = x. Calculate the value of x.

Diagram for this question
  1. A.70°
  2. B.58°
  3. C.55°
  4. D.48°
Show the answer and explanation

Answer: B (58°)

Explanation

∠QPR = ∠QRT = 52° (alternate segment). In triangle PQR, x = 180° − 70° − 52° = 58°.