The question in the image is asking which angles are supplementary, given that lines $IK$ and $LN$ are parallel.

Supplementary angles are two angles whose measures add up to $180^\circ$.

Let's analyze the angles:

From the diagram:

• $IK \parallel LN$ (parallel lines)
• $HJ$ is a transversal crossing both lines $IK$ and $LN$.

Using the properties of parallel lines and a transversal, the following pairs of angles are supplementary:

1. $\angle IJH$ and $\angle KJM$: These are same-side interior angles, which are supplementary because the transversal $HJ$ intersects the parallel lines.

Thus, the correct answer is $\angle IJH$ and $\angle KJM$. These two angles add up to $180^\circ$ because they are on the same side of the transversal.

Would you like more details or have any questions?

Here are five relative questions for further understanding:

1. What are complementary angles, and how do they differ from supplementary angles?
2. Can you identify vertical angles in the diagram?
3. What is the relationship between alternate interior angles?
4. How do you know that $IK \parallel LN$?
5. What is the sum of all interior angles around a point?

Tip: When dealing with parallel lines, remember that same-side interior angles are always supplementary.