Question

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

Answer 1

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.