The diagram in the image shows two parallel lines $l$ and $t$, which are cut by two transversals, $m$ and $s$. The angles formed at the intersections are numbered for reference. Let's work through the examples requested for each type of angle pair based on this setup:

1. Corresponding angles: These are angles that are in the same position at each intersection where a transversal crosses two lines. For example, angle 1 and angle 5 are corresponding angles.

2. Alternate interior angles: These are angles that are on opposite sides of the transversal but inside the two lines. An example is angle 6 and angle 9.

3. Alternate exterior angles: These are angles on opposite sides of the transversal but outside the two lines. An example is angle 1 and angle 12.

4. Consecutive interior angles: These are angles on the same side of the transversal and inside the two lines. An example is angle 6 and angle 10.

5. Vertical angles: These are pairs of angles that are opposite each other at the intersection of two lines. For example, angle 4 and angle 15 are vertical angles.

6. Linear pair: A linear pair consists of two adjacent angles whose non-common sides form a straight line. For example, angle 9 and angle 10 form a linear pair.

Would you like more details on any of these? Here are 5 related questions to expand your understanding:

1. Can you identify another pair of corresponding angles from the diagram?
2. How are alternate interior angles used to prove lines are parallel?
3. What is the relationship between alternate exterior angles and the lines being parallel?
4. What do we know about the measures of consecutive interior angles if the lines are parallel?
5. Can you list more pairs of vertical angles from the diagram?

Tip: Always remember that corresponding angles are congruent when the lines are parallel. This can help you identify and solve for unknown angles easily.