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GCE Mathematics 1990 Question 30

Question 30

Triangles and Quadrilaterals

In the diagram below, |PQ| = |PR| = |RS| and ∠RPS = 32°. Find the value of ∠QPR.

Diagram for this question
  1. A.72°
  2. B.64°
  3. C.52°
  4. D.32°
  5. E.26°
Show the answer and explanation

Answer: C (52°)

Explanation

Triangle PRS is isosceles, so ∠RSP = 32° and the exterior angle ∠PRQ = 32° + 32° = 64°. Triangle PQR is isosceles, so ∠PQR = 64° and ∠QPR = 180° − 128° = 52°.