To solve the question, we need to recall that supplementary angles are two angles whose sum equals 180°. In the diagram, supplementary angles often appear as adjacent angles formed by intersecting lines.

Let's examine the pairs of angles mentioned:

1. ∠KLN and ∠MLN:

   • These are adjacent angles on a straight line $KLMN$. Since they are formed along a straight line, they are supplementary. Their sum is 180°.

2. ∠JIG and ∠KLN:

   • These two angles are not adjacent, nor do they share a straight line, so they are not supplementary.

3. ∠KLI and ∠MLN:

   • These angles are adjacent at point $L$, and they are on opposite sides of a straight line, making them supplementary (since they sum up to 180°).

4. ∠KLI and ∠JIL:

   • These angles are adjacent but not on a straight line, so they do not add up to 180°. Hence, they are not supplementary.

From this analysis, the pairs of supplementary angles are:

• ∠KLN and ∠MLN (correct)
• ∠KLI and ∠MLN (correct)

Would you like further details on supplementary angles or clarification on any step?

Here are 5 follow-up questions to explore more:

1. How do we determine if two angles are supplementary on a complex figure?
2. Can supplementary angles exist without being adjacent?
3. What is the difference between complementary and supplementary angles?
4. How does the concept of linear pairs relate to supplementary angles?
5. In what cases do supplementary angles appear in geometry problems?

Tip: When dealing with intersecting lines, look for angles that form a straight line (180°), as they are most likely supplementary.