Question

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

Answer 1

Determine the minimum interior angle possible for a regular polygon.

Assume a regular polygon having the least number of sides.

Since, an equilateral triangle is a regular polygon with the least number of sides.

The sum of all the angles of a triangle is $180°$ degrees.

$\begin{array}{rcl}x+x+x& =& 180°\\ & \Rightarrow & 3x=180°\\ & \Rightarrow & x=\frac{180°}{3}\\ & \Rightarrow & x=60°\end{array}$

Hence, the minimum interior angle possible for a regular polygon is $60°$.