Chapter 2.6, Problem 8CE

To determine

To describe: Plan for proving $\angle 3\cong \angle 4$

Explanation of Solution

Given:

The given figure is,

  

And the condition is,

  $\angle 3$ is supplementary to angle $\angle 1$ and

  $\angle 4$ is supplementary to angle $\angle 2$

As given,

  $\angle 3$ is supplementary to angle $\angle 1$

So, $m\angle 3+m\angle 1=180$ ...... (1)

And $\angle 4$ is supplementary to angle $\angle 2$

So, $m\angle 4+m\angle 2=180$ ...... (2)

Now, $m\angle 1=m\angle 2$ (Alternate opposite angles)

From (1) and (2)

  $\begin{array}{l}m\angle 3+m\angle 1=m\angle 4+m\angle 2\\ \Rightarrow m\angle 3=m\angle 4\left(\text{Since, }m\angle 1=m\angle 2\right)\end{array}$

Hence, $\angle 3\cong \angle 4$