Question

A polygon is such that the sum of its interior angle is thrice the sum of the exterior angle. Find the number of sides

Answer 1

Let the polygon have $n$ sides. The sum of the interior angles of an $n$-gon is $180(n-2)$ degrees, and the sum of the exterior angles is always 360 degrees. Therefore, we have the equation:

$$180(n-2) = 3 \cdot 360$$

Simplifying, we get:

$$n-2 = 6$$

$$n = \boxed{8}$$

So the polygon has 8 sides