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

Question

Philoid · Accepted Answer

To find the maximum exterior angle of a regular polygon, we will have to take the lowest possible number of sides (i.e., an equilateral triangle).

Now,

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

Exterior angle of an equilateral triangle = 360^o/3

= 120^o

Hence, the maximum possible measure of exterior angle for any polygon is 120^o.

And, we know that an exterior angle and an interior angle are always in a linear pair

Hence, minimum interior angle = 180^o − 120°

= 60^o