Chapter 12, Problem 2CT

To determine

To find :the $m\angle 2$ if they are vertical angles and when $m\angle 1={81}^{\circ }$ .

Answer to Problem 2CT

  $m\angle 2$ is ${99}^{\circ }$ when they are vertical angles and $m\angle 1={81}^{\circ }$

Explanation of Solution

Given :

  $m\angle 1={81}^{\circ }$ .

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

We know that thevertical angles sum is ${180}^{\circ }$ ,

  $\begin{array}{l}m\angle 1+m\angle 2={180}^{\circ }\\ {81}^{\circ }+m\angle 2={180}^{\circ }\text{ [substitute]}\\ m\angle 2={180}^{\circ }-{81}^{\circ }\text{ [subtract]}\\ m\angle 2={99}^{\circ }\end{array}$

Hence, $m\angle 2$ is ${99}^{\circ }$ when they are vertical angles and $m\angle 1={81}^{\circ }$.