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WAEC Mathematics 2012 Question 44

Question 44

Triangles and Quadrilaterals

In the diagram, |SR| = |QR|, ∠SRP = 65° and ∠RPQ = 48°, find ∠PRQ.

Diagram for this question
  1. A.65°
  2. B.45°
  3. C.25°
  4. D.19°
Show the answer and explanation

Answer: D (19°)

Explanation

∠RSQ = ∠RPQ = 48° (same segment), and ΔSRQ is isosceles, so ∠RQS = 48° and ∠SRQ = 84°. ∠PRQ = 84° − 65° = 19°.