Given:
Line ST is perpendicular to line PR.
![m\angle PQV=32^\circ](/tpl/images/1234/3726/44af7.png)
To find:
The measure of angle SQU.
Solution:
Line ST is perpendicular to line PR.
![m\angle SQR=90^\circ](/tpl/images/1234/3726/63a7d.png)
If two lines intersect each other, then the vertically opposite angles are equal.
(Vertically opposite angle)
![m\angle UQR=32^\circ](/tpl/images/1234/3726/454f6.png)
Now,
![m\angle SQR=m\angle SQU+m\angle UQR](/tpl/images/1234/3726/25be5.png)
![90^\circ=m\angle SQU+32^\circ](/tpl/images/1234/3726/54add.png)
![90^\circ-32^\circ=m\angle SQU](/tpl/images/1234/3726/f8187.png)
![58^\circ=m\angle SQU](/tpl/images/1234/3726/c5f38.png)
Therefore, the correct option is D.