The sum of the interior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon.

Let n be the number of sides of the polygon.

By formula,

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

Sum of exterior angles of a polygon = 360°.

Given,

The sum of the interior angles of a polygon is four times the sum of its exterior angles.

⇒ (2n - 4) × 90° = 4 × 360°

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

⇒ (2n - 4) = 4 × 4

⇒ 2n - 4 = 16

⇒ 2n = 16 + 4

⇒ 2n = 20

⇒ n = $\dfrac{20}{2}$ = 10.

Hence, number of sides in polygon = 10.