Chapter 2, Problem 8RP

To determine

To Prove: $\angle C$ is supplement to $\angle D$

Explanation of Solution

Given information: $\angle A$ is supplementary to $\angle D$ and $\angle A\cong \angle C$ is provided in the question which will help to find the solution.

Proof: Here, $\angle A$ is supplementary to $\angle D$ (as given in the question)

So, $\angle A+\angle D={180}^{\circ }$ (Given)

and, $\angle A\cong \angle C$ (Given)

So that, we can say that

  $\angle C+\angle D={180}^{\circ }$

Hence, $\angle C$ is supplement to $\angle D$