Question

How can we find the number of side and interior angles if We have exterior angle?

Answer 1

We will learn how to find the sum of the exterior angles of a polygon having n sides.

We know that, exterior angle + interior adjacent angle = 180°

So, if the polygon has n sides, then

Sum of all exterior angles + Sum of all interior angles = n × 180°

So, sum of all exterior angles = n × 180° - Sum of all interior angles

Sum of all exterior angles = n × 180° - (n -2) × 180°

= n × 180° - n × 180° + 2 × 180°

= 180°n - 180°n + 360°

= 360°

Therefore, we conclude that sum of all exterior angles of the polygon having n sides = 360°

Therefore, measure of each exterior angle of the regular polygon = 360°/n

Also, number of sides of the polygon = 360°/each exterior angle

Solved examples on sum of the exterior angles of a polygon:

1. Find the number of sides in a regular polygon when the measure of each exterior angle is 45°.

Solution:

If the polygon has n sides,

Then, we know that; n = 360°/measure of each exterior angle

= 360/45

= 8

Therefore, the regular polygon has 8 sides.