Question

angle bisector or perpendicular bisector marked?
neither
perpendicular bisector
both
angle bisector

Explanation:

Step1: Check perpendicular bisector condition

Segment $PR$ divides $SQ$ into two equal parts (each length 5), and $PR \perp SQ$, so $PR$ is a perpendicular bisector.

Step2: Check angle bisector condition

Set the angle measures equal: $5x-20 = 3x+10$
Solve for $x$:
$5x - 3x = 10 + 20$
$2x = 30$
$x = 15$
Substitute $x=15$: $5(15)-20=55$, $3(15)+10=55$. So $PR$ bisects $\angle SPQ$, meaning it is an angle bisector.

Answer:

Both