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WAEC Mathematics 2000 Question 27

Question 27

Angles and Polygons

In the diagram, POS and ROT are straight lines. OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

Diagram for this question
  1. A.160°
  2. B.140°
  3. C.120°
  4. D.100°
Show the answer and explanation

Answer: D (100°)

Explanation

Triangle OST is isosceles, so ∠SOT = 180 − 100 = 80°, and ∠POR = 80° (vertically opposite). Adjacent angles of a parallelogram add to 180°, so ∠OPQ = 100°.