Chapter 11.1, Problem 20IP

To determine

To find: $\angle 1$

Answer to Problem 20IP

  $m\angle 1={127.4}^0$

Explanation of Solution

Given information:

  $m\angle 6={52.6}^0$

From the given figure

We can say that $\angle 6$ and $\angle 8$ are Supplementary angles.

As we know sum of their measures is ${180}^0$ .

  $\begin{array}{l}\angle 6+\angle 8={180}^0\\ \Rightarrow {52.6}^0+\angle 8={180}^0\\ \Rightarrow \angle 8={180}^0-{52.6}^0\\ \Rightarrow \angle 8={127.4}^0\end{array}$

Since $\angle 8$ and $\angle 1$ are alternate exterior angles, they are congruent.

So,

  $\angle 1={127.4}^0$

Therefore,

  $m\angle 1={127.4}^0$