# What is the maximum exterior angle possible for a regular polygon?

Answer

Verified

361.5k+ views

Hint: Sum of exterior of a regular polygon = ${360^{^0}}$. Use the equilateral triangle, which has maximum measures and where we know that triangle is the simplest polygon.

Let us consider a polygon with minimum number of side i.e. = $3$

As we know that triangle is simple polygon with number of sides =3

We know that Exterior angles of an equilateral triangle have the maximum measure.

And we also know that,

Sum of exterior angle of polygon = ${360^{^0}}$$ \to (1)$

Let us consider each exterior angle as $A$

By using $(1)$ we can write

$ \Rightarrow $$A + A + A = {360^0}$

$ \Rightarrow 3A = {360^0}$

$

\Rightarrow A = \dfrac{{{{360}^0}}}{3} \\

\Rightarrow A = {120^0} \\

$

Therefore, the maximum exterior angle possible for regular polygon =${120^0}$

Note: Focus on the angle given i.e. exterior or interior angles which includes maximum or minimum value.

Let us consider a polygon with minimum number of side i.e. = $3$

As we know that triangle is simple polygon with number of sides =3

We know that Exterior angles of an equilateral triangle have the maximum measure.

And we also know that,

Sum of exterior angle of polygon = ${360^{^0}}$$ \to (1)$

Let us consider each exterior angle as $A$

By using $(1)$ we can write

$ \Rightarrow $$A + A + A = {360^0}$

$ \Rightarrow 3A = {360^0}$

$

\Rightarrow A = \dfrac{{{{360}^0}}}{3} \\

\Rightarrow A = {120^0} \\

$

Therefore, the maximum exterior angle possible for regular polygon =${120^0}$

Note: Focus on the angle given i.e. exterior or interior angles which includes maximum or minimum value.

Last updated date: 15th Sep 2023

â€¢

Total views: 361.5k

â€¢

Views today: 9.61k