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

Last updated date: 27th Mar 2023
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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.