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WAEC Mathematics 2011 Question 47

Question 47

Angles and Polygons

In the diagram, PQ//TS, PR//TU, reflex angle QPS = 245°, angle PST = 115°, ∠STU = 65° and ∠RPS = x. Find the value of x.

Diagram for this question
  1. A.80°
  2. B.70°
  3. C.60°
  4. D.50°
Show the answer and explanation

Answer: D (50°)

Explanation

∠QPT (inside) = 360° − 245° = 115°. Since PQ ∥ TS and PR ∥ TU, ∠QPR = ∠STU = 65°. So x = 115° − 65° = 50°.