Question

Which diagram shows lines that must be parallel lines cut by a transversal?

2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 65 degrees.
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees and the bottom right angle is 65 degrees.
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the top right angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 115 degrees.
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the uppercase left angle is 65 degrees and the bottom right angle is 65 degrees.

Answer 1

Diagrams 1 and 3.

- Diagram 1: the angles given (115° and 65°) are same-side interior angles and sum to 180°, so the lines must be parallel.
- Diagram 3: the two 115° angles are alternate exterior angles; equal alternate exterior angles force the lines to be parallel.

Diagrams 2 and 4 do not force parallelism (2 shows a linear pair at one intersection; 4 shows vertical angles).