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WAEC Mathematics 2014 Question 15

Question 15

Triangles and Quadrilaterals

In the diagram, ∠QPT = ∠PTS = 90°, ∠PQR = 110° and ∠TSR = 20°. Find the size of the obtuse angle QRS.

Diagram for this question
  1. A.140°
  2. B.130°
  3. C.120°
  4. D.110°
Show the answer and explanation

Answer: B (130°)

Explanation

PQRST is a pentagon, so its angles add to 540°: the reflex angle at R = 540° − 90° − 90° − 110° − 20° = 230°. The obtuse angle QRS = 360° − 230° = 130°.