How many sides has a regular polygon whose interior angles are 120°each

Analyze the question: We need the number of sides of a regular polygon when each interior angle is 120°.

Concept: In a regular polygon with n sides, the interior angle and the exterior angle sit on a straight line, so:

Interior angle + Exterior angle = 180°

The sum of all exterior angles of any polygon is 360°, so each exterior angle of a regular polygon is 360°/n.

Solution:

1. Exterior angle = 180° − 120° = 60°
2. Number of sides: n = 360° / 60° = 6

Check with the interior angle formula: Interior angle = (n − 2) × 180° / n = (6 − 2) × 180° / 6 = 4 × 180° / 6 = 120° ✓

The polygon is a regular hexagon, so the answer is C. 6.

Tip: For "each interior angle" questions, find the exterior angle first (180° − interior), then divide 360° by it. It is much faster than solving (n − 2) × 180 / n = angle. Also remember: 60° exterior gives 6 sides, 90° gives 4, 120° gives 3.