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WAEC Mathematics 2013 Question 37

Question 37

Angles and Polygons

In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of ∠RVS.

Diagram for this question
  1. A.36°
  2. B.54°
  3. C.60°
  4. D.72°
Show the answer and explanation

Answer: A (36°)

Explanation

Each exterior angle of a regular pentagon is 360° ÷ 5 = 72°. In triangle RVS, ∠VRS = ∠VSR = 72°, so ∠RVS = 180° − 144° = 36°.