Let's analyze the diagram and answer the questions related to whether the given angles form a linear pair, vertical angles, or neither.

Definitions:

• Linear pair: Two adjacent angles whose non-common sides are opposite rays, forming a straight line. Their sum is $180^\circ$.
• Vertical angles: Two angles formed by two intersecting lines, opposite each other. Vertical angles are always congruent.

Based on the image:

We have a figure with two intersecting lines, forming five labeled angles: $\angle 1, \angle 2, \angle 3, \angle 4,$ and $\angle 5$.

Answers for each question:

23. $\angle 2$ and $\angle 5$:
These angles are vertical angles because they are opposite each other where two lines intersect.
Answer: Vertical.

24. $\angle 1$ and $\angle 5$:
These angles form a linear pair since they are adjacent and their non-common sides form a straight line.
Answer: Linear pair.

25. $\angle 1$ and $\angle 3$:
These angles do not form a linear pair or vertical angles, as they are neither adjacent nor opposite each other.
Answer: Neither.

Would you like further explanations for any of these concepts? Here are some related questions:

1. How can you determine if two angles are supplementary?
2. What is the relationship between adjacent angles in a linear pair?
3. How do we know that vertical angles are congruent?
4. What is the difference between complementary and supplementary angles?
5. Can two adjacent angles also be vertical angles?

Tip: Always look for intersecting lines to identify vertical angles quickly!