91Ó°ÊÓ

The supplementary angles are the angles whose sum is 180°.

As the angles$∠1$ and$∠2$ are the supplementary angles, therefore the sum of the angles$∠1$ and$∠2$ is 180°.

$$\begin{gathered} \begin{array}{c}∠1+∠2=180\\ 27+∠2=180\end{array} \\ ∠2=180-27 \\ ∠2=153 \end{gathered}$$

Therefore, the measure of the angle$∠2$ is 153°.

As the angles$∠3$ and$∠4$ are the supplementary angles, therefore the sum of the angles$∠3$ and$∠4$ is 180°.

$$\begin{gathered} \begin{array}{c}∠3+∠4=180\\ 27+∠4=180\end{array} \\ \begin{array}{c}∠4=180-27\\ ∠4=153\end{array} \end{gathered}$$

Therefore, the measure of the angle$∠4$ is 153°.

The supplementary angles are the angles whose sum is 180°.

As the angles$∠1$ and$∠2$ are the supplementary angles, therefore the sum of the angles$∠1$ and$∠2$ is 180°.

$$\begin{gathered} \begin{array}{c}∠1+∠2=180\\ x+∠2=180\end{array} \\ ∠2=180-x \end{gathered}$$

Therefore, the measure of the angle$∠2$ is $\left(180-x\right)°$.

As the angles$∠3$ and$∠4$ are the supplementary angles, therefore the sum of the angles$∠3$ and$∠4$ is 180°.

$$\begin{gathered} \begin{array}{c}∠3+∠4=180\\ x+∠4=180\end{array} \\ ∠4=180-x \end{gathered}$$

Therefore, the measure of the angle$∠4$ is $\left(180-x\right)°$.

The supplementary angles are the angles whose sum is 180°.

As the angles $∠1$and $∠2$are the supplementary angles, therefore the sum of the angles $∠1$and $∠2$is 180°.

$∠1+∠2=180\left(1\right)$

As the angles $∠3$and $∠4$are the supplementary angles, therefore the sum of the angles $∠3$and $∠4$is 180°.

$∠3+∠4=180\left(2\right)$

Subtract the equation (2) from equation (1).

$\begin{array}{c}∠1+∠2-\left(∠3+∠4\right)=180-180\\ ∠1+∠2-∠3-∠4=0\left(3\right)\end{array}$

Consider the two angles$∠1$ and$∠3$ be congruent angles.

Therefore, $∠1=∠3$.

Substitute the above values in the equation (3).

$$\begin{gathered} \begin{array}{c}∠1+∠2-∠3-∠4=0\\ ∠1+∠2-∠1-∠4=0\end{array} \\ \begin{array}{c}∠2-∠4=0\\ ∠2=∠4\end{array} \end{gathered}$$

As, the angles $∠2$and $∠4$have same measure therefore the angles $∠2$and $∠4$are congruent angles.

The angles $∠2$and $∠4$are supplements of the angles $∠1$and $∠3$respectively.

The angles $∠1$and $∠3$are congruent angles then the angles $∠2$and $∠4$are also congruent angles.

Therefore, if the angles are congruent then the supplements of the angles are also congruent.