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WAEC Mathematics 2003 Question 26

Question 26

Triangles and Quadrilaterals

In the diagram, ∠PQS = 65°, ∠RPS = 40° and ∠QSR = 20°. Find ∠PSQ.

Diagram for this question
  1. A.85°
  2. B.60°
  3. C.55°
  4. D.45°
Show the answer and explanation

Answer: C (55°)

Explanation

∠QPR = ∠QSR = 20° (same arc QR), so ∠QPS = 20 + 40 = 60°. In triangle PQS, ∠PSQ = 180 − 65 − 60 = 55°.