91Ó°ÊÓ

The given diagram is:

The congruent angles are the angles which have same measure.

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

From the given diagram it can be noticed that the angles$∠AXB$ and$∠BXD$ forms the linear pair.

Therefore, the sum of the angles$∠AXB$ and$∠BXD$ is$180°$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠AXB+∠BXD=180° \\ 90°+∠BXD=180° \\ ∠BXD=180°−90° \\ ∠BXD=90° \end{gathered}$$

Therefore,$∠BXD=90°$

Therefore, it can be noticed that:

$∠AXB=∠BXD=90°$

It can also be noticed that $∠AXB+∠BXD=180°$.

Therefore, as$∠AXB+∠BXD=180°$ and $∠AXB=∠BXD=90°$.

Therefore, the angles$∠AXB$ and$∠BXD$ are congruent supplementary angles.

Therefore, the two congruent supplementary angles are$∠AXB$ and $∠BXD$.

The given diagram is:

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

From the given diagram it can be noticed that the angles$∠AXC$ and$∠CXD$ forms the linear pair.

Therefore, the sum of the angles$∠AXC$ and$∠CXD$ is $180°$.

From the diagram it can also be noticed that the angles$∠AXC$ and$∠CXD$ do not have same measure.

Therefore, the angles$∠AXC$ and$∠CXD$ are not congruent.

As, the sum of the angles $∠AXC$and $∠CXD$is $180°$and the angles $∠AXC$and $∠CXD$are not congruent.

Therefore, the two supplementary angles that are not congruent are$∠AXC$ and $∠CXD$.

The given diagram is:

The complementary angles are the angles whose sum is $90°$.

From the given diagram it can be noticed that the angles$∠AXB$ and$∠BXD$ forms the linear pair.

Therefore, the sum of the angles$∠AXB$ and$∠BXD$ is$180°$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠AXB+∠BXD=180° \\ 90°+∠BXD=180° \\ ∠BXD=180°−90° \\ ∠BXD=90° \end{gathered}$$

Therefore,$∠BXD=90°$

By using the angle addition postulate, it can be said that:

$∠BXC+∠CXD=∠BXD$

Therefore, it can be obtained that:

$$\begin{gathered} ∠BXC+∠CXD=∠BXD \\ ∠BXC+∠CXD=90° \end{gathered}$$

As,,$∠BXC+∠CXD=90°$ therefore the angles$∠BXC$ and$∠CXD$ are complementary angles.

The two complementary angles are$∠BXC$and $∠CXD$.

The given diagram is:

A straight angle is an angle which has measure of $\mathbf{180}\mathbf{°}$.

From the given diagram it can be noticed that the angle$∠AXD$ has measure of $180°$.

Therefore, the angle$∠AXD$ is a straight angle.