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WAEC Mathematics 1993 Question 22

Question 22

Triangles and Quadrilaterals

In the diagram below, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30° and ∠PQR = 80°. Find ∠SPQ.

Diagram for this question
  1. A.15°
  2. B.25°
  3. C.40°
  4. D.50°
  5. E.55°
Show the answer and explanation

Answer: B (25°)

Explanation

Join PR. In isosceles triangle PSR, ∠SPR = (180° − 30°)/2 = 75°. In isosceles triangle PQR, ∠QPR = (180° − 80°)/2 = 50°. So ∠SPQ = 75° − 50° = 25°.