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WAEC Mathematics 1998 Question 48

Question 48

Triangles and Quadrilaterals

In the diagram below, |PQ| = |PR| = |RS| and ∠RSP = 35°. Find ∠QPR.

Diagram for this question
  1. A.70°
  2. B.50°
  3. C.45°
  4. D.40°
  5. E.35°.
Show the answer and explanation

Answer: D (40°)

Explanation

PR = RS, so ∠RPS = ∠RSP = 35° and the exterior angle ∠PRQ = 70°. PQ = PR, so ∠PQR = 70° too, and ∠QPR = 180 − 140 = 40°.