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JAMB Mathematics 1993 Question 31

Question 31

Circle Theorems

In the figure above, PT is a tangent to the circle at U and QU ‖ RS. If ∠TUR = 35° and ∠SRU = 50°, find ∠x.

Diagram for this question
  1. A.95°
  2. B.85°
  3. C.50°
  4. D.35°
Show the answer and explanation

Answer: A (95°)

Explanation

By the alternate segment theorem, angle UQR = angle TUR = 35°. Since QU ‖ RS, angle QUR = angle URS = 50° (alternate angles). In triangle QUR, x = 180° − 35° − 50° = 95°.