Chapter 12, Problem 1CT

To determine

To find :the value of $m\angle 2$ , where $m\angle 1={64}^{\circ }$ and both angles are supplementary.

Answer to Problem 1CT

the value of $m\angle 2$ is ${116}^{\circ }$ where $m\angle 1={64}^{\circ }$ .

Explanation of Solution

Given : consider, the figure provided in the question,

  $m\angle 1={64}^{\circ }$

Both angles are supplementary angles.

Calculation: we know that the sum of supplementary angles is ${180}^{\circ }$ , angles are supplementary, then substitute $m\angle 1={64}^{\circ }$ then subtract each side by ${64}^{\circ }$ ,

So

  $\begin{array}{l}m\angle 1+m\angle 2={180}^{\circ }\\ {64}^{\circ }+m\angle 2={180}^{\circ }\\ m\angle 2={180}^{\circ }-{64}^{\circ }\\ m\angle 2={116}^{\circ }\end{array}$

Hence,the value of $m\angle 2$ is ${116}^{\circ }$ where $m\angle 1={64}^{\circ }$ .