The given image involves two parallel lines, $\overleftrightarrow{PR}$ and $\overleftrightarrow{SU}$, with a transversal line intersecting them. We are tasked with determining which angles are supplementary.

In geometry, supplementary angles are two angles that add up to $180^\circ$. Given the parallel lines, we can use the concept of consecutive interior angles, which are supplementary when a transversal intersects two parallel lines.

Upon examining the angles:

• $\angle UTV$ and $\angle STQ$ are consecutive interior angles formed by the transversal $\overleftrightarrow{QT}$, so they are supplementary.

Thus, the correct answer is:

• $\angle UTV$ and $\angle STQ$ are supplementary angles.

Would you like any further details on supplementary angles or transversal geometry? Feel free to ask!

Related Questions:

1. How do you identify supplementary angles in parallel lines?
2. What is the difference between alternate interior angles and consecutive interior angles?
3. Can vertical angles be supplementary?
4. What other types of angle relationships occur with parallel lines and transversals?
5. How does the concept of parallel lines and a transversal apply in real-life situations?

Tip: Remember that when two parallel lines are cut by a transversal, alternate interior angles and consecutive interior angles exhibit specific relationships like congruence and supplementarity.