The angle bisectors of APQR are PZ, QZ, and RZ. They meet at a single point Z. (In other words, Z is the incenter of APQR.)
Suppose WZ=10, QZ=13,
mwQX=96°, and mZYRZ=22°.
m
Find the following measures.
Note that the figure is not drawn to scale.

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?