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

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

Let the exterior angle of the polygon be a.

Then the interior angle is 3a.

As we know, the sum of the interior angle and the exterior angle is 180°.

⇒ a + 3a = 180°

⇒ 4a = 180°

⇒ a = $\dfrac{180°}{4}$

⇒ a = 45°

So, the exterior angle is 45°.

The interior angle is 3a = 3 x 45° = 135°.

Each interior angle of a regular polygon can be calculated using the formula: $\dfrac{(2n - 4) \times 90°}{n}$

⇒ 135° = $\dfrac{(2n - 4) \times 90°}{n}$

By cross multiplying, we get

⇒ 135°n = (2n - 4) 90°

⇒ 135°n = 180°n - 360°

⇒ 180°n - 135°n = 360°

⇒ 45°n = 360°

⇒ n = $\dfrac{360°}{45°}$

⇒ n = 8

Hence, the number of sides is 8.