Chapter 12.3, Problem 49E

To determine

To find :themeasure of an exterior angle for the pentagon which is obtain in the 20cent euro.

Answer to Problem 49E

the measure of an exterior angle for the pentagon which is obtain in the 20 cent euro is ${51.42}^{\circ }$ .

Explanation of Solution

Given : consider, the polygon provided in the question,

7-gon.

Formula used:

Each exterior angle for a regular n-gon has measure equal to $\frac{{360}^{\circ }}{n}$ .

Calculation: for the 20 cent euro, the obtain polygon is 7-gon so substitute n by 7 in the formula and divide.

The measure of an exterior angle of a regular 7-gon = $\begin{array}{l}\frac{{360}^{\circ }}{7}\\ {51.42}^{\circ }\text{ [divide]}\end{array}$

Hence,the measure of an exterior angle for the pentagon which is obtain in the 20 cent euro is ${51.42}^{\circ }$ .