Each interior angle of a regular polygon is double of its exterior angle, the number of sides in the polygon is.

1. 3

2. 4

3. 6

4. 8

It is given that each interior angle of a regular polygon is double of its exterior angle.

Let the exterior angle of the polygon be a.

Then the interior angle is 2a.

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

⇒ a + 2a = 180°

⇒ 3a = 180°

⇒ a = $\dfrac{180°}{3}$

⇒ a = 60°

So, the exterior angle is 60° and the interior angle is:

2a = 2 x 60° = 120°

The formula for each interior angle of a regular polygon is:

$\dfrac{(2n - 4) \times 90°}{n}$

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

By cross multiplying, we get

⇒ 120°n = (2n - 4) 90°

⇒ 120°n = 180°n - 360°

⇒ 180°n - 120°n = 360°

⇒ 60°n = 360°

⇒ n = $\dfrac{360°}{60°}$

⇒ n = 6

Hence, option 3 is the correct option.