To determine which angle is supplementary to a given angle in a figure of parallel lines cut by a transversal, we first need to recall that supplementary angles are two angles whose sum is $180^\circ$.

Since no specific angle is given in the question, I will assume you’re asking which angle is supplementary to the angle you're inquiring about. Typically, when parallel lines are cut by a transversal:

1. Consecutive interior angles are supplementary (they sum to $180^\circ$).
2. Linear pairs (angles that form a straight line) are also supplementary.

If you can clarify which angle you're referring to, I can tell you which angle is supplementary to it. For now, without knowing the exact figure, I can only provide general rules.

Would you like to provide more information about the figure, or clarify which angle you're asking about?

---

Further Exploration:

1. What are alternate interior angles and how are they related in parallel lines?
2. How do corresponding angles behave in parallel lines cut by a transversal?
3. What are consecutive exterior angles in parallel lines cut by a transversal?
4. How do you calculate the angle measure given one angle and knowing they are supplementary?
5. What is the difference between complementary and supplementary angles?

Tip: In parallel lines cut by a transversal, alternate interior angles are equal, and consecutive interior angles are supplementary.