Let's solve the problem step by step, referring to the image you've provided:

(a) One pair of vertical angles:

Vertical angles are the angles opposite each other when two lines intersect. From the figure, angles $2$ and $6$ are vertical angles because they are opposite each other at the intersection of lines $l$ and $m$.

So, one pair of vertical angles is: $\angle 2 \text{ and } \angle 6$

(b) One pair of angles that form a linear pair:

A linear pair consists of two adjacent angles that sum up to 180° because they form a straight line. In the diagram, angles $3$ and $4$ are adjacent and form a linear pair.

Thus, one pair of angles that form a linear pair is: $\angle 3 \text{ and } \angle 4$

(c) One pair of angles that are supplementary:

Supplementary angles are two angles whose measures add up to 180°. As we discussed above, angles that form a linear pair are supplementary. Therefore, angles $3$ and $4$ are also a pair of supplementary angles.

So, one pair of supplementary angles is: $\angle 3 \text{ and } \angle 4$

Summary:

• (a) Vertical angles: $\angle 2$ and $\angle 6$
• (b) Linear pair: $\angle 3$ and $\angle 4$
• (c) Supplementary angles: $\angle 3$ and $\angle 4$

Would you like more details on any part of this solution, or further explanation? Here are some related questions for practice:

1. Can you identify another pair of vertical angles from the figure?
2. Can you find another pair of angles that form a linear pair?
3. Why are linear pairs always supplementary?
4. What is the sum of the angles in a linear pair?
5. How do complementary and supplementary angles differ?

Tip: When identifying vertical angles, remember they always appear in pairs at the intersection of two straight lines.