The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.

It is given that the sum of interior angles of a regular polygon is twice the sum of its exterior angles.

Let the sum of the exterior angles be a.

Then, the sum of the interior angles is 2a.

We know that sum of the interior angle and the exterior angle is 180°.

⇒ 2a + a = 180°

⇒ 3a = 180°

⇒ a = $\dfrac{180°}{3}$

⇒ a = 60°

Thus:

Exterior angle = a = 60°

Interior angle = 2a = 2 x 60° = 120°

According to the properties of polygons, each interior angle of a regular polygon with n sides is $\dfrac{(2n - 4) \times 90°}{n}$.

⇒ $\dfrac{(2n - 4) \times 90°}{n}$ = 120°

By cross-multiplying, we get

⇒ (2n - 4) x 90° = 120°n

⇒ 180°n - 360° = 120°n

⇒ 180°n - 120°n = 360°

⇒ 60°n = 360°

⇒ n = $\dfrac{360°}{60°}$

⇒ n = 6

Hence, the number of sides is 6.