Chapter 11.3, Problem 37HP

To determine

To write: The change in interior angle of regular polygon if number of sides increases by 1.

Answer to Problem 37HP

Increase by ${180}^{\circ }$

Explanation of Solution

Given: A regular polygon of sides n

A regular polygon of sides n.

The sum of angles of polygons $=\left(n-2\right){180}^{\circ }$

If the number of sides increase by 1 .

Therefore new sides become $n+1$

The sum of angles of new polygon $=\left(n+1-2\right){180}^{\circ }$

Now arrange the expression.

  $\begin{array}{l}=\left(n-2\right){180}^{\circ }+{180}^{\circ }\\ ={\text{Sum of angles of old polygon+180}}^{\circ }\end{array}$

Hence, sum of angles of polygon increases by ${180}^{\circ }$