In this diagram, corresponding angles are pairs of angles that occupy the same relative position at each intersection where a transversal crosses parallel lines. Here, line $PQ$ is parallel to line $SU$, and $QR$ is the transversal.

To identify corresponding angles, let's focus on the options provided:

1. $\angle UTQ$ and $\angle STQ$
2. $\angle UTQ$ and $\angle RQO$
3. $\angle UTQ$ and $\angle PQO$
4. $\angle UTQ$ and $\angle PQT$

The correct answer is option 2: $\angle UTQ$ and $\angle RQO$. These two angles are in corresponding positions relative to the transversal $QR$.

Would you like a deeper explanation on why these angles are corresponding, or do you have further questions?

Here are five related questions to expand on this topic:

1. What defines corresponding angles in parallel lines and transversals?
2. How can we identify alternate interior angles in this setup?
3. What is the significance of angle relationships when parallel lines are cut by a transversal?
4. How are consecutive interior angles different from corresponding angles?
5. Why are corresponding angles always equal in measure when lines are parallel?

Tip: When identifying corresponding angles, visualize shifting one of the intersecting lines along the transversal to see which angles overlap in position.