To determine the relationship between angles ∠2 and ∠7 in a situation where two parallel lines are intersected by a transversal, we need to understand the positioning of these angles.
- Alternate Interior Angles: Angles that are on opposite sides of the transversal and inside the two parallel lines.
- Alternate Exterior Angles: Angles that are on opposite sides of the transversal and outside of the two parallel lines.
- Supplementary Angles: Two angles that add up to 180 degrees.
- Vertical Angles: Angles that are opposite each other when two lines intersect.
If ∠2 and ∠7 are situated such that one is on one side of the transversal and the other is on the opposite side but both are located between the two parallel lines, then they are Alternate Interior Angles.
If they are positioned such that they are both outside the parallel lines and on opposite sides of the transversal, then they would be Alternate Exterior Angles.
In most situations involving two parallel lines and a transversal, angles labeled in a specific pattern will often be either alternate interior or alternate exterior angles. Given the standard labeling of angles near parallel lines, it is likely that if ∠2 and ∠7 fall into the category described above, they would be classified as Alternate Interior Angles.
So, the answer is B. Alternate interior angles if they are between the two lines and on opposite sides of the transversal.