Question

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

Explanation:

Step1: Recall parallel - line properties

When parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to 180°), corresponding angles are equal, and alternate interior angles are equal.

Step2: Analyze the first diagram

In the first diagram, the 115° and 65° angles are consecutive interior angles. Since 115°+65° = 180°, by the converse of the consecutive - interior - angles postulate, the lines must be parallel.

Step3: Analyze the second diagram

In the second diagram, the 115° and 65° angles are not in a position (like consecutive interior, corresponding, or alternate interior) that would guarantee the lines are parallel just from these angle measures.

Answer:

The first diagram shows lines that must be parallel lines cut by a transversal.