Question

What is the common angle of pqt and rsq

Answer 1

Are you at GACA?
If so the answers to the quick check are:

1. A
2. D
3. D
4. B 
5. D

Answer 2

I think the image you were referring to is this:
This image shows two triangles that intersect each other at a common angle. The two triangle are triangle PQT and triangle RSQ.  Both triangles meet at a common angle, and that is angle Q, or in other words,  angle PQR