Chapter 2.6, Problem 10CE

To determine

To describe: Plan for proving $m\angle 2=m\angle 3$

Explanation of Solution

Given:

The given figure is,

  

And the condition is,

  $m\angle 1=m\angle 4$

As from the figure,

  $\angle 1$ is supplementary to angle $\angle 2$

So, $m\angle 1+m\angle 2=180$ ....... (1)

Also,

  $\angle 3$ is supplementary to angle $\angle 4$

So, $m\angle 3+m\angle 4=180$ ....... (2)

From (1) and (2)

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

Hence, $m\angle 2=m\angle 3$