In a regular polygon, the interior angle exceeds the corresponding exterior…

Concept

At each vertex of a regular polygon, the interior angle I and the corresponding exterior angle E are supplementary: I + E = 180°. The exterior angles sum to 360°, so for n sides, E = 360° ÷ n.

Application

1. Let the interior angle be I and the corresponding exterior angle be E. The condition gives I − E = 60°.

2. Use I + E = 180° together with I − E = 60°. Adding the equations gives 2I = 240°, hence I = 120° and E = 60°.

3. Since E = 360° ÷ n, n = 360° ÷ 60° = 6.

Cross-check

For a 6-sided regular polygon, the interior angle is (6 − 2) × 180° ÷ 6 = 120° and the exterior angle is 360° ÷ 6 = 60°. Their difference is 60°, as required.

Therefore, the polygon has 6 sides.