Chapter 2.4, Problem 2PSA

To determine

To Prove: $\angle 1\cong \angle 2.$

Explanation of Solution

Given information: $\angle 1$ is supplementary to $\angle 2$ and $\angle 2$ is supplementary to $\angle 3.$

Formula used: sum of an angle and its supplement is ${180}^{\circ }$

Proof: $\because \angle 1$ is supplementary to $\angle 2$

  $\because \angle 1+\angle 2={180}^{\circ }\mathrm{....}(1)$

Also, $\angle 2$ is supplementary to $\angle 3$ ,

  $\therefore \angle 2+\angle 3={180}^{\circ }\mathrm{....}(2)$

From equation (1) and (2),

  $\begin{array}{l}\angle 1+\angle 2=\angle 2+\angle 3\\ \therefore \angle 1=\angle 3.\end{array}$