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WAEC Mathematics 1992 Question 21

Question 21

Triangles and Quadrilaterals

In the diagram below, TR = TS and ∠TRS = 60°. Find the value of x.

Diagram for this question
  1. A.30
  2. B.45
  3. C.60
  4. D.120
  5. E.150
Show the answer and explanation

Answer: C (60)

Explanation

TR = TS with ∠TRS = 60° makes triangle RST equilateral, so ∠RST = 60° and ∠PSR = 180° − 60° = 120°. PSRQ is cyclic, so x = 180° − 120° = 60°.