Question

Line ST is perpendicular to line PR.

What is the measure of ZSQU?
90°

32°

148°

58°

Answer 1

Given:

Line ST is perpendicular to line PR.

`m\angle PQV=32^\circ`

To find:

The measure of angle SQU.

Solution:

Line ST is perpendicular to line PR.

`m\angle SQR=90^\circ`

If two lines intersect each other, then the vertically opposite angles are equal.

`m\angle UQR=m\angle PQV` (Vertically opposite angle)

`m\angle UQR=32^\circ`

Now,

`m\angle SQR=m\angle SQU+m\angle UQR`

`90^\circ=m\angle SQU+32^\circ`

`90^\circ-32^\circ=m\angle SQU`

`58^\circ=m\angle SQU`

Therefore, the correct option is D.