Why is 120 degrees the highest exterior angle for a regular polygon?

Solution:

In a regular polygon, all angles are equal and all sides are equal.

For any regular polygon, an angle formed between any side and an adjacent side extended is known as an exterior angle. Let's take a few examples to understand what is an exterior angle.

For any regular polygon, the sum of all the exterior angles is 360 degrees.

Let's see some examples using the below diagram

To find the value of the highest exterior angle for a regular polygon, we must divide 360 degrees by the number of sides of that polygon.

1) Triangle:

Number of sides = 3

Value of each exterior angle = 360º/3 = 120º

2) Quadrilateral:

Number of sides = 4

Value of each exterior angle = 360º/4 = 90º

3) Pentagon:

Number of sides = 5

Value of each exterior angle = 360º/5 = 72º

We just saw that if we keep on increasing the number of sides, the highest exterior angle value will decrease. Hence to get the highest exterior angle we need to take a polygon with the least number of sides, which is a triangle with 3 sides.

Therefore, 120º is the highest exterior angle for a regular polygon.

Why is 120 degrees the highest exterior angle for a regular polygon?

Summary:

The polygon with the least number of sides has the highest exterior angle. For any regular polygon the measure of each angle can be obtained by dividing 360º by the number of sides. The triangle is the polygon with the least number of sides, and hence 120º is the highest exterior angle for a regular polygon (equilateral triangle).