Question

which diagram shows parallel lines cut by a transversal?

Explanation:

Step1: Recall parallel - lines and transversal properties

When parallel lines are cut by a transversal, corresponding angles are congruent, alternate - interior angles are congruent, and same - side interior angles are supplementary.

Step2: Analyze the first diagram

In the first diagram, the angles given ($75^{\circ}$ and $80^{\circ}$) do not follow the angle - relationships of parallel lines cut by a transversal.

Step3: Analyze the second diagram

In the second diagram, the angles $85^{\circ}$ and $81^{\circ}$ do not follow the angle - relationships of parallel lines cut by a transversal.

Step4: Analyze the third diagram

In the third diagram, the angles $130^{\circ}$ and $50^{\circ}$ are supplementary (since $130 + 50=180$). This is a property of same - side interior angles when parallel lines are cut by a transversal.

Answer:

The third diagram