WAEC 2011 Mathematics · Question 21

A regular polygon of n sides has each exterior angle to 45o. Find the value of n

Options

A.6
B.8
C.12
D.15

Answer: B. 8

Explanation written with AI and checked against the answer key

Analyze the question: We have a regular polygon whose exterior angles are each 45°. We need the number of sides, n. Concept: The sum of the exterior angles of any polygon (convex) is always 360°. In a regular polygon, all exterior angles are equal, so: Each exterior angle = 360° ÷ n Solution: 45° = 360° ÷ n n = 360° ÷ 45° n = 8 Check: Each interior angle = 180° − 45° = 135°. The interior angle sum formula gives (n − 2) × 180° ÷ n = (6 × 180°) ÷ 8 = 135°, which matches. ✔ Correct answer: B (8) Tip: For any regular polygon, remember n = 360° ÷ exterior angle. Also, interior angle + exterior angle = 180°. These two facts solve most polygon questions in WASSCE, JAMB and NECO quickly.

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