Chapter 3, Problem 11CR

To determine

To prove : The congruency of $\angle 6$ with respect to $\angle 8$ .

Explanation of Solution

Given information : Here, we have given that $\angle 6$ is supplementary to $\angle 7$

Proof: Supplementary angles are the angles whose sum is $180°$ .

As, $\angle 6$ is supplementary to $\angle 7$ ,

  $\begin{array}{l}\Rightarrow \angle 6+\angle 7\cong 180°\\ \Rightarrow \angle 6\cong 180°-\angle 7\end{array}$

And, $\angle 7+\angle 8\cong 180°$ (Linear Pair Angles)

  $\Rightarrow \angle 8\cong 180°-\angle 7$

Now as, $\angle 6\cong 180°-\angle 7$ and $\angle 8\cong 180°-\angle 7$

  $\Rightarrow \angle 6\cong \angle 8$