Chapter 12.3, Problem 19E

To determine

To find :theunknown angle.

Answer to Problem 19E

The unknown angle is ${78}^{\circ }$ .

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,

  $\begin{array}{l}{x}^{\circ }+{75}^{\circ }+{104}^{\circ }+{103}^{\circ }={360}^{\circ }\text{ [subtitute the angles]}\\ x^{\circ }+{282}^{\circ }={360}^{\circ }\text{ [add]}\\ x^{\circ }={360}^{\circ }-{282}^{\circ }\text{ [subtract]}\\ x^{\circ }={78}^{\circ }\end{array}$

Hence, The unknown angle is ${78}^{\circ }$ .