NECO 2004 Mathematics · Question 25

One of the interior angles of a regular polygon is 120°. Find the number of sides of the polygon

Options

A.3
B.4
C.6
D.9
E.12

Answer: C. 6

Explanation written with AI and checked against the answer key

Analyze the question: We have a regular polygon (all sides and all angles equal) with each interior angle equal to 120°. We need the number of sides, n. Concept: Interior and exterior angles at each vertex lie on a straight line, so they add up to 180°. The exterior angles of any polygon sum to 360°, so for a regular polygon: Each exterior angle = 360° / n Solution: Step 1: Find the exterior angle. Exterior angle = 180° − 120° = 60° Step 2: Use the exterior angle formula. 360° / n = 60° n = 360° / 60° = 6 Check with the interior angle formula: Interior angle = (n − 2) × 180° / n (6 − 2) × 180° / 6 = 4 × 180° / 6 = 720° / 6 = 120° ✓ The polygon is a regular hexagon with 6 sides. Tip: For regular polygons, go through the exterior angle first: n = 360° ÷ (180° − interior angle). It's much faster than solving (n − 2) × 180 / n algebraically. Useful values to remember: 60° interior gives 3 sides, 90° gives 4, 108° gives 5, 120° gives 6.

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