Answer:
B) <2≅<6
Explanation:
When a transversal crosses over 2 parallel lines there are certain statements that can be made, such as the fact that corresponding angles are congruent.
Defining a Corresponding Angle
Corresponding angles are angles that have the same relative position with different vertices. For example, if 2 angles are both in the bottom left of an intersection of 2 lines, they are corresponding. Since both angle 2 and 6 are in the top right, they are corresponding.
Proving the Lines are Parallel
Since corresponding angles are congruent when a transversal crosses parallel lines, any statement that proves corresponding angles are congruent would prove the lines are parallel. This means that <2≅<6 must prove that l║m.
Process of Elimination
Additionally, we can prove that B is correct by proving that the other answers are incorrect.
A) Angle 2 and 3 are vertical angles. This has nothing to do with parallel lines and cannot be used to prove that l║m.
C) Angle 7 and 8 are a linear pair, and, once again, this has nothing to do with whether or not l and m are parallel.
D) If l and m were parallel, then angles 3 and 5 would sum to 180 degrees. this is because if l║m, then <3 and <5 would be same side interior angles. Same side interior angles always sum to 180. So, this statement would actually disprove l║m.