Chapter 2, Problem 9RP

To determine

To Prove: The congruency of $\angle 1$ with respect to $\angle 2$

Explanation of Solution

Given information: $\angle 1\cong \angle 3$ provided in the question which will help to find the solution.

Formula used: Here, we are using the linear angle theorem.

Proof: Here, $\angle 3+\angle 4={180}^{\circ }$ (linear angle property)

So, $\angle 1+\angle 4={180}^{\circ }$ ( $\because$

  $\angle 1=\angle 3$ )

Also, $\angle 2+\angle 4={180}^{\circ }$ (linear angle property)

Hence, by using congruence rule, we can say that

  $\angle 1\cong \angle 2$