https://file.aiquickdraw.com/mathbot/file/17268527431067pb7jivb.jpg

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.

For the figure below, give the following:
(a) one pair of vertical angles
(b) one pair of angles that form a linear pair
(c) one pair of angles that are supplementary

Learn how to identify vertical angles, linear pairs, and supplementary angles from a geometric figure. This problem covers key geometric concepts including the Vertical Angle Theorem and the Linear Pair Postulate, suitable for students in Grades 6-8.

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