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WAEC Mathematics 1996 Question 38

Question 38

Triangles and Quadrilaterals

The trapezium PQRS has /PS/ = /PQ/, PQ is parallel to SR, <PQS = 34° and <SPQ = 2<SRQ. Find the size of <SQR

Diagram for this question
  1. A.58°
  2. B.68°
  3. C.78°
  4. D.90°
  5. E.112°
Show the answer and explanation

Answer: D (90°)

Explanation

PS = PQ, so <PSQ = 34° and <SPQ = 180° − 68° = 112°, which makes <SRQ = 56°. <QSR = <PQS = 34° (alternate angles), so in triangle SQR, <SQR = 180° − 34° − 56° = 90°.