Question

The sum of the angles of a polygon and the sum of its external angles are equal. How many sides does it have?

Answer 1

Given: Sum of the external angles of a polygon is equal to the sum of its internal angles.

We know that in a polygon, the sum of all the external angles = 360°

Also, the sum of the angles of a polygon with n sides = (n −2) × 180°

⇒360° = (n −2) × 180°

⇒ n −2 = 2

⇒ n = 4

Thus, a polygon with four sides has the sum of the internal angles equal to the sum of its external angles.