Given:
Line ST is perpendicular to line PR.
[tex]m\angle PQV=32^\circ[/tex]
To find:
The measure of angle SQU.
Solution:
Line ST is perpendicular to line PR.
[tex]m\angle SQR=90^\circ[/tex]
If two lines intersect each other, then the vertically opposite angles are equal.
[tex]m\angle UQR=m\angle PQV[/tex] (Vertically opposite angle)
[tex]m\angle UQR=32^\circ[/tex]
Now,
[tex]m\angle SQR=m\angle SQU+m\angle UQR[/tex]
[tex]90^\circ=m\angle SQU+32^\circ[/tex]
[tex]90^\circ-32^\circ=m\angle SQU[/tex]
[tex]58^\circ=m\angle SQU[/tex]
Therefore, the correct option is D.