Let's go over the angle pairs and their relationships based on the diagram.

Key Observations:

• $HJ \parallel KM$
• Line $LI$ is the transversal crossing both parallel lines.

Let's analyze each pair:

1. $\angle MLI$ and $\angle JIL$:
   These angles are on the same side of the transversal $LI$ and are interior angles between the two parallel lines.
   Answer: 5. Same-side interior angles

2. $\angle KLI$ and $\angle HIG$:
   These angles are both on the upper left and lower right of the transversal, corresponding in the same relative position on the two parallel lines.
   Answer: 2. Corresponding angles

3. $\angle HIL$ and $\angle MLI$:
   These angles are outside the parallel lines but on opposite sides of the transversal $LI$.
   Answer: 3. Alternate exterior angles

4. $\angle KLN$ and $\angle HIG$:
   These angles are on opposite sides of the transversal $LI$ and between the parallel lines.
   Answer: 4. Alternate interior angles

5. $\angle MLN$ and $\angle HIG$:
   These angles are on the same side of the transversal and outside the parallel lines.
   Answer: 1. Same-side exterior angles

Summary of matches:

1. $\angle MLI$ and $\angle JIL$ → 5. Same-side interior angles
2. $\angle KLI$ and $\angle HIG$ → 2. Corresponding angles
3. $\angle HIL$ and $\angle MLI$ → 3. Alternate exterior angles
4. $\angle KLN$ and $\angle HIG$ → 4. Alternate interior angles
5. $\angle MLN$ and $\angle HIG$ → 1. Same-side exterior angles

Would you like more details or have any other questions?

Here are 5 related questions you can explore:

1. What are alternate exterior angles, and how can you identify them?
2. Can corresponding angles be congruent in any case?
3. How do same-side interior angles help in proving parallel lines?
4. What is the significance of the transversal in determining angle relationships?
5. How do alternate interior angles help in real-world construction?

Tip: When analyzing angle relationships with parallel lines, always look for the transversal first to simplify the identification process.