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WAEC Mathematics 2017 Question 50

Question 50

Circle Theorems

In the diagram, RP is a diameter of circle RSP, RP is produced to T and TS is a tangent to the circle as S. If ∠PRS = 24°, calculate the value of ∠STR.

Diagram for this question
  1. A.24°
  2. B.42°
  3. C.48°
  4. D.66°
Show the answer and explanation

Answer: B (42°)

Explanation

∠RSP = 90° (semicircle) and ∠PST = ∠PRS = 24° (alternate segment), so ∠RST = 114°. In triangle RST, ∠STR = 180° − 24° − 114° = 42°.