Question

(a) What is the minimum interior angle possible for a regular polygon?

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

Answer 1

Consider a regular polygon having the lowest possible number of sides.

Clearly it is an equilateral triangle.

Each interior angle of a triangle is ${60}^{\circ }$ [Since, $\frac{{180}^{\circ }}{3}={60}^{\circ }$]

$\Rightarrow$ the minimum interior angle possible for a regular polygon is ${60}^{\circ }$. ---(a)

The exterior angle of this triangle will be the maximum exterior angle possible for any regular polygon.

Exterior angle of an equilateral triangle $=\frac{{360}^{\circ }}{3}={120}^{\circ }$

[Since, Each exterior angle of regular polygon with '$n$'-sides is $\frac{{360}^{\circ }}{n}$]

Hence, maximum possible measure of exterior angle for any polygon is ${120}^{\circ }$.----(b)