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WAEC Mathematics 1992 Question 19

Question 19

Circle Theorems

In the diagram above PQT is a tangent to the circle QRS at Q. Angle QTR = 48° and ∠QRT = 95°. Find ∠QSR

Diagram for this question
  1. A.48°
  2. B.45°
  3. C.37°
  4. D.32°
  5. E.30°
Show the answer and explanation

Answer: C (37°)

Explanation

In triangle QRT, ∠RQT = 180° − 48° − 95° = 37°. By the alternate segment theorem, ∠QSR = ∠RQT = 37°.