WAEC 2024 Mathematics · Question 6

The interior angle of a regular polygon is 168º. Find the number of sides of the polygon.

Options

A.24
B.30
C.15
D.12

Answer: B. 30

Explanation written with AI and checked against the answer key

Analyze the question: We're told each interior angle of a regular polygon is 168° and must find the number of sides, n. Concept: The interior and exterior angles at a vertex lie on a straight line, so they add up to 180°. The exterior angles of any polygon add up to 360°, so for a regular polygon: Exterior angle = 360° / n Solution: Step 1: Find the exterior angle. Exterior angle = 180° − 168° = 12° Step 2: Use the exterior angle formula. 360° / n = 12° n = 360° / 12° = 30 Check using the interior angle formula: Interior angle = (n − 2) × 180° / n = (30 − 2) × 180° / 30 = 28 × 6° = 168° ✓ Answer: The polygon has 30 sides, which is option B. Tip: When you're given an interior angle of a regular polygon, go straight to the exterior angle (180° − interior) and divide 360° by it. It's much faster than solving (n − 2) × 180 / n = angle. Also, note that 15 (option C) would give an interior angle of 156°, so it's a trap for students who slip in the calculation.

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