Chapter 12.3, Problem 20E

To determine

To find :theunknown angle

Answer to Problem 20E

The unknown angle is ${42}^{\circ }$ .

Explanation of Solution

Given : consider, the figureprovided in the question,

Formula used: the sum of all exterior angle = ${360}^{\circ }$

Calculation: put the values of all exterior angles in the formula then add and subtract,

  $\begin{array}{l}{x}^{\circ }+{81}^{\circ }+{68}^{\circ }+{79}^{\circ }+{90}^{\circ }={360}^{\circ }\text{ [substitute the angles]}\\ x^{\circ }+{318}^{\circ }={360}^{\circ }\text{ [add]}\\ x^{\circ }={360}^{\circ }-{318}^{\circ }\text{ [subtract]}\\ x^{\circ }={42}^{\circ }\end{array}$

Hence,The unknown angle is ${42}^{\circ }$ .