Chapter 2, Problem 6RP

To determine

To Prove: The congruency of the $\angle 2$ with respect to $\angle 3$

Explanation of Solution

Given information: $\angle 1\cong \angle 4$ provided in the question which will help to find the solution.

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

Proof: Here, $\angle 1\cong \angle 4$ (as given in the question)

and, $\angle 1+\angle 2={180}^{\circ }$ (Linear pair)

So, $\angle 2={180}^{\circ }-\angle 1$ ………. $\left(1\right)$

and, $\angle 3+\angle 4={180}^{\circ }$ (Linear pair)

So, $\angle 3={180}^{\circ }-\angle 4$ ………... $\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$ , we get

In equation $\left(2\right)$ , $\angle 3={180}^{\circ }-\angle 4$ ( $\because$

  $\angle 1\cong \angle 4$ )

So that, $\angle 3={180}^{\circ }-\angle 1$ (which is equal to equation 1)

Hence, $\angle 2\cong \angle 3$