91Ó°ÊÓ

The given diagram is:

It is being given that$∠VTR$is a right angle.

Therefore, $∠VTR=90°$.

From the given diagram it can be noticed that the angles $∠VTR$and $∠VTP$form the linear pair.

Therefore, the sum of the angles $∠VTR$and $∠VTP$is $180°$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠VTR+∠VTP=180° \\ 90°+∠VTP=180° \\ ∠VTP=180°−90° \\ ∠VTP=90° \end{gathered}$$

The measure of the angle $∠VTP$is $90°$.

The given diagram is:

It is being given that$m∠QSR=60$.

From the given diagram it can be noticed that the angles$∠QSR$ and$∠XSY$ are the vertically opposite angles.

Therefore, $∠XSY=∠QSR$.

Therefore, it can be obtained that:

$\begin{array}{c}∠XSY=∠QSR\\ =60°\end{array}$

The measure of the angle$∠XSY$ is$60°$.

The given diagram is:

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

Therefore, sum of the angles$∠RSX$ and$∠XSY$ is$180°$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠RSX+∠XSY=180° \\ ∠RSX+60°=180° \\ ∠RSX=180°−60° \\ ∠RSX=120° \end{gathered}$$

The measure of the angle$∠RSX$ is $120°$.

The given diagram is:

It is being given thatthe four angles of figure$PQRS$ are right angles.

Therefore, it can be said that $∠PSR=90°$.

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

Therefore, the sum of the angles$∠PSR$ and$∠PSY$ is$180°$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠PSR+∠PSY=180° \\ 90°+∠PSY=180° \\ ∠PSY=180°−90° \\ ∠PSY=90° \end{gathered}$$

The measure of the angle$∠PSY$ is $90°$.