Chapter 12, Problem 3CT

To determine

To find:the $m\angle 2$ if they are complementary angles and when $m\angle 1={77}^{\circ }$ .

Answer to Problem 3CT

  $m\angle 2$ is ${13}^{\circ }$ when they are complementary angles and $m\angle 1={77}^{\circ }$

Explanation of Solution

Given : the anglesprovided in the question,

  $m\angle 1={77}^{\circ }$ .

Calculation: to find the $m\angle 2$ ,

We know that thecomplementary angles sum is ${90}^{\circ }$ ,

  $\begin{array}{l}m\angle 1+m\angle 2={70}^{\circ }\\ {77}^{\circ }+m\angle 2={180}^{\circ }\text{ [substitute]}\\ m\angle 2={180}^{\circ }-{77}^{\circ }\text{ [subtract]}\\ m\angle 2={13}^{\circ }\end{array}$

Hence, $m\angle 2$ is ${13}^{\circ }$ when they are vertical angles and $m\angle 1={77}^{\circ }$.