Answer:
B
Explanation:
Let's take a look at each statement.
A: ∠1 ≅ ∠8
Angle 1 is congruent to angle 8.
If lines are parallel then angle 1 and angle 8 would be same side (consecutive) exterior angles which are supplementary and not congruent.
Therefore this statement would prove that the lines are not parallel.
B: ∠1 ≅ ∠7
Angle 1 is congruent to angle 7.
If lines are parallel then angle 1 and angle 7 would be alternate exterior angles which are congruent.
This statement proves that the lines are parallel. We have angle 1 that is at line AB and angle 7 which is at line CD. It's important that one angle is at one line and the second angle at the other line, otherwise we cannot prove that the lines are parallel.
C: ∠6 ≅ ∠8
Angle 6 is congruent to angle 8.
Angles 6 and 8 are vertical angles and they are congruent.
This statement is correct but it doesn't tell us anything about the relationship of angles at the other line, therefore it proves nothing.
D: ∠1 and ∠2 are supplementary.
Angles 1 and 2 create a linear pair, therefore they are supplementary.
This statement is also correct but again it tells us nothing about the angles at the other line so it again proves nothing.