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WAEC Mathematics 2008 Question 45

Question 45

Angles and Polygons

In the diagram, ∠QPR = 60°, ∠PQR = 50°, ∠QRS = 2x°, ∠SRP = 3x°, ∠UQP = y° and RS // TU. Calculate y.

Diagram for this question
  1. A.102°
  2. B.78°
  3. C.70°
  4. D.60°
Show the answer and explanation

Answer: A (102°)

Explanation

In ΔPQR, 5x = 180 − 60 − 50 = 70, so x = 14 and ∠QRS = 28°. RS ∥ TU gives ∠TQR = 28° (alternate). On the straight line UQT: y + 50 + 28 = 180, so y = 102°.