Chapter 12, Problem 2CST

To determine

To find :the $\angle 3and\angle 4$ if they are supplementary.

Answer to Problem 2CST

  $\angle 3and\angle 4$ is ${97}^{\circ }and{83}^{\circ }$ when they are supplementary.

Explanation of Solution

Given :

  $\begin{array}{l}m\angle 3={110}^{\circ }\\ m\angle 4={110}^{\circ }\end{array}$

  $\begin{array}{l}m\angle 3={97}^{\circ }\\ m\angle 4={83}^{\circ }\end{array}$

  $\begin{array}{l}m\angle 3={57}^{\circ }\\ m\angle 4={33}^{\circ }\end{array}$

  $\begin{array}{l}m\angle 3={82}^{\circ }\\ m\angle 4={41}^{\circ }\end{array}$

Calculation: to find the $\angle 3and\angle 4$ add the angles given in the options, for supplementary angles their sum will be ${180}^{\circ }$ .

In options,

  $\begin{array}{l}m\angle 3+m\angle 4={97}^{\circ }+{83}^{\circ }\\ m\angle 3+m\angle 4=180\end{array}$

Hence, $\angle 3and\angle 4$ is ${97}^{\circ }and{83}^{\circ }$ when they are supplementary