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WAEC Mathematics 2008 Question 20

Question 20

Triangles and Quadrilaterals

In the diagram, |PQ| = |QR| and |PR| = |RS| = |SP|. Calculate the size of ∠QRS.

Diagram for this question
  1. A.150°
  2. B.120°
  3. C.90°
  4. D.60°
Show the answer and explanation

Answer: C (90°)

Explanation

ΔPRS is equilateral, so ∠PSR = ∠PRS = 60°. PQRS is cyclic, so ∠PQR = 180° − 60° = 120°, and the isosceles ΔPQR has ∠QRP = 30°. ∠QRS = 30° + 60° = 90°.