In the given diagram, we are asked to identify a pair of alternate exterior angles and name the two lines and the transversal that form the pair.

Step-by-step analysis:

1. Understanding Alternate Exterior Angles: Alternate exterior angles are formed when a transversal crosses two parallel lines. They are located on opposite sides of the transversal and outside the parallel lines.

2. Labeling the Diagram:

   • Lines $a \parallel b$ are parallel lines.
   • Line $c$ is the transversal cutting through $a$ and $b$.

   The angles outside of the two parallel lines are labeled as:

   • Exterior angles on the left: $\angle 1$ and $\angle 8$
   • Exterior angles on the right: $\angle 2$ and $\angle 7$

3. Identifying Alternate Exterior Angles:

   • From the definition, we know that alternate exterior angles must be on opposite sides of the transversal (line $c$).
   • $\angle 1$ (left of transversal) is alternate to $\angle 8$ (right of transversal).
   • $\angle 2$ (left of transversal) is alternate to $\angle 7$ (right of transversal).

Answer:

The correct pair of alternate exterior angles from the options provided is $\angle 2$ and $\angle 7$, which matches option B.

Let me know if you'd like more details or have further questions.

Here are 5 related questions you can explore:

1. What are alternate interior angles in the same diagram?
2. How do you prove that two lines are parallel using alternate exterior angles?
3. What is the relationship between alternate exterior angles and corresponding angles?
4. Can alternate exterior angles be supplementary? Why or why not?
5. How can the concept of alternate exterior angles be applied in real-life situations?

Tip: Remember that alternate exterior angles are always congruent if the lines are parallel.