Chapter 2, Problem 22RP

To determine

To Prove: The congruency of the $\angle 1$ with respect to $\angle 4$

Explanation of Solution

Given information: $\angle 1$ is complement to $\angle 3$ and $\angle 4$ is complement to $\angle 2$ is provided in the question which will help to find the solution.

Formula used: Sum of complementary angles is ${90}^{\circ }$

Proof: Here, $\angle 1+\angle 3={90}^{\circ }$ (given)

And, $\angle 2+\angle 4={90}^{{}^{\circ }}$ (given)

So that, $\angle 1+\angle 3=\angle 2+\angle 4$

And, $\angle 2=\angle 3$ (vertically opposite angles)

So that, $\angle 1+\angle 3=\angle 3+\angle 4$

  $\angle 1=\angle 4$

So, by congruency rule we can say that

  →$\angle 1\cong \angle 4$