Point A is the incenter of △PQR. Find each measure

AU=20 units

Step-by-step explanation:

We are given that

AT=20 units

Point A is the incenter of triangle PQR.

Incenter is that point where three angle bisector of triangle meets.

AR is the bisector of angle R of triangle PQR.

Therefore,

All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.

Right angled triangle ATP and Right triangle AUP are similar.

Therefore,

units

AP is the angle bisector  of angle P of triangle PQR

Using the value of angle x

Hence, the measure of angle QPA=35 degree