Chapter 12, Problem 10CST

To determine

To find: The value of $x$ .

Answer to Problem 10CST

The value of $x$ is ${16}^{\circ }$ .

Explanation of Solution

Given information: The measures of a pentagon’s exterior angles, one exterior angle at each vertex, are ${67}^{\circ },{\text{ 102}}^{\circ },{\text{ 131}}^{\circ },{\text{ 28}}^{\circ }\text{ and 2}{x}^{\circ }$ .

Calculation: A pentagon is a five sided polygon, there are five exterior angles in a pentagon.

Sum of the five exterior angles of a pentagon is $={360}^{\circ }$

Therefore, ${67}^{\circ }{\text{+ 102}}^{\circ }{\text{+ 131}}^{\circ }{\text{+ 28}}^{\circ }\text{ + 2}{x}^{\circ }={360}^{\circ }$$\mathrm{......}(1)$

Let’s solve the equation $(1)$ to find the value of $x$ ,

  $\begin{array}{c}{67}^{\circ }{\text{+ 102}}^{\circ }{\text{+ 131}}^{\circ }{\text{+ 28}}^{\circ }\text{ + 2}{x}^{\circ }={360}^{\circ }\\ {328}^{\circ }+2x^{\circ }={360}^{\circ }\\ 2x^{\circ }={360}^{\circ }-{328}^{\circ }\\ x=\frac{{32}^{\circ }}{2}\\ x={16}^{\circ }\end{array}$

Hence, The value of $x$ is ${16}^{\circ }$ .