To solve this problem:

Identifying Supplementary Angles:

• Supplementary angles are two angles whose measures add up to $180^\circ$.
  From the figure:
• $\angle 1$ and $\angle 2$ are supplementary because they are adjacent angles on a straight line.

Identifying Vertical Angles:

• Vertical angles are the non-adjacent angles formed when two lines intersect.
  From the figure:
• $\angle 2$ and $\angle 4$ are vertical angles because they are opposite each other at the intersection of the lines.

Final Answers:

1. Supplementary Angles: $\angle 1$ and $\angle 2$
2. Vertical Angles: $\angle 2$ and $\angle 4$

Would you like a deeper explanation of supplementary and vertical angles?

Related Questions:

1. What are complementary angles, and how are they different from supplementary angles?
2. Can you identify another pair of supplementary angles in the figure?
3. What makes vertical angles congruent?
4. How can you identify linear pairs of angles in the diagram?
5. Why do vertical angles always have the same measure?

Tip:

When two lines intersect, always look for angles that are opposite to each other to find vertical angles. For supplementary angles, check for pairs of adjacent angles forming a straight line.