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WAEC Mathematics 1991 (August) Question 44

Question 44

Triangles and Quadrilaterals

In the diagram below, ∠PTQ = ∠URP = 25° and XPU = 4URP. Calculate ∠USQ.

Diagram for this question
  1. A.100°
  2. B.120°
  3. C.125°
  4. D.130°
  5. E.150°
Show the answer and explanation

Answer: D (130°)

Explanation

∠XPU = 100°, so ∠UPQ = 80°. In triangle PTQ, ∠PQT = 180° − 80° − 25° = 75°, so ∠SQR = 105°. In triangle SQR, ∠QSR = 180° − 105° − 25° = 50°, so ∠USQ = 180° − 50° = 130°.