Chapter 6.1, Problem 44PPS

(a)

To determine

The measures of each interior angle in the given figure.

Answer to Problem 44PPS

The measure of each interior angle is 154.3.

Explanation of Solution

Given:

The given figure is:

It is a regular 14-sided polygon.

Calculation:

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

The given figure is a 14-gon, therefore, it has 14 congruent interior angles. Angles supplementary to congruent angles are also congruent, hence the exterior angles are congruent.

Let the measure of each exterior angle be n.

So,

  $\begin{array}{l}14n=360\\ n=\frac{360}{14}\\ n=25.7\end{array}$

Let the measure of each interior angle be m.

The interior angle and the exterior angle form a linear pair.

So,

  $\begin{array}{l}m+n=180\\ m=180-n\\ m=180-25.7\\ m=154.3\end{array}$

The measure of each interior angle is 154.3.

(b)

To determine

The measures of each exterior angle in the given figure.

Answer to Problem 44PPS

The measure of each exterior angle is 25.7

Explanation of Solution

Given:

The given figure is:

It is a regular 14-sided polygon.

Calculation:

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

The given figure is a 14-gon, therefore, it has 14 congruent interior angles. Angles supplementary to congruent angles are also congruent, hence the exterior angles are congruent.

Let the measure of each exterior angle be n.

So,

  $\begin{array}{l}14n=360\\ n=\frac{360}{14}\\ n=25.7\end{array}$