Chapter 6.1, Problem 39PPS

To determine

The measure of an exterior angle and an interior angle of each regular polygon.

Answer to Problem 39PPS

The measure of each exterior angle is 51.4. and the measure of each interior angle is 128.6.

Explanation of Solution

Given:

The given polygon has 7 sides.

Calculation:

The sum of the measures of exterior angles of a convex polygon, one angle at each vertex is 360.

Also, in a regular 7-gon, there are 7 congruent interior angles.

The exterior angles of a 7-gon are also congruent as angles supplementary to congruent angles are also congruent.

Suppose, the measure of each exterior angle be n.

Therefore,

  $\begin{array}{l}7n=360\\ n=\frac{360}{7}\\ n=51.4\end{array}$

Suppose, the measure of each interior angle be m.

So, $m+n=180$ , as an interior angle and an exterior angle make a linear pair.

Therefore,

  $\begin{array}{l}m=180-n\\ m=180-51.4\\ m=128.6\end{array}$

The measure of each exterior angle is 51.4. and the measure of each interior angle is 128.6.