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 :

1. 14

2. 10

3. 12

4. 16

Let n be the number of sides of the polygon.

By formula,

Sum of interior angles of an 'n' sided regular polygon = (2n - 4) × 90°.

Sum of exterior angles of a regular polygon = 360°.

Given,

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

∴ (2n - 4) × 90° = 6 × 360°

⇒ 2n - 4 = $\dfrac{6 \times 360°}{90°}$

⇒ 2n - 4 = 6 × 4

⇒ 2n - 4 = 24

⇒ 2n = 24 + 4

⇒ 2n = 28

⇒ n = $\dfrac{28}{2}$ = 14.

Hence, Option 1 is the correct option.