Question

The sum of the interior angles of a regular polygon is equal to six times the sum of its exterior angles. The number of sides of the polygon is ______.

Options

• 14

• 10

• 12

• 16

Answer 1

The sum of the interior angles of a regular polygon is equal to six times the sum of its exterior angles. The number of sides of the polygon is 12.

Explanation:

The sum of the interior angles of an n-sided polygon is (n − 2) × 180°, and the sum of its exterior angles is always 360°. Setting the interior angle sum equal to six times the exterior angle sum gives (n − 2) × 180° = 6 × 360°, which simplifies to n − 2 = 12, resulting in n = 12.