Question

applying angle relationships to justify parallel lines
which diagram shows parallel lines cut by a transversal?

Explanation:

Step1: Recall the property of parallel lines cut by a transversal

When parallel lines are cut by a transversal, consecutive - interior angles are supplementary (sum to \(180^{\circ}\)).

Step2: Check the first diagram

The angles \(85^{\circ}\) and \(81^{\circ}\) are not supplementary (\(85 + 81=166
eq180\)).

Step3: Check the second diagram

The angles \(75^{\circ}\) and \(80^{\circ}\) are not supplementary (\(75 + 80 = 155
eq180\)).

Step4: Check the third diagram

The angles \(130^{\circ}\) and \(50^{\circ}\) are supplementary (\(130+50 = 180\)).

Answer:

The third diagram.