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WAEC Mathematics 2007 Question 23

Question 23

Triangles and Quadrilaterals

In the diagram, |SP| = |SR| and ∠PRS = 50°. Calculate ∠PQR.

Diagram for this question
  1. A.120°
  2. B.110°
  3. C.100°
  4. D.80°
Show the answer and explanation

Answer: C (100°)

Explanation

Triangle PSR is isosceles, so ∠SPR = 50° and ∠PSR = 180° − 100° = 80°. PQRS is cyclic, so ∠PQR = 180° − 80° = 100°.