Question

1. determine which lines, if any, are parallel. 8. determine which lines, if any, are parallel

Explanation:

Step1: Recall parallel - line criteria

If corresponding angles are equal, or alternate - interior angles are equal, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze angles for the first set of lines

For lines \(a\), \(b\), \(c\), and \(d\) in the first diagram:
The \(140^{\circ}\) angle and the \(40^{\circ}\) angle are supplementary. Let's assume the transversal intersects lines \(a\) and \(c\). The \(140^{\circ}\) angle and the \(40^{\circ}\) angle are same - side interior angles. Since \(140^{\circ}+40^{\circ}=180^{\circ}\), by the same - side interior angles postulate, \(a\parallel c\).

Step3: Analyze angles for the second set of lines

In the second diagram, assume the transversal intersects lines \(x\), \(y\), and \(z\).
We have angles \(115^{\circ}\) and \(65^{\circ}\). Since \(115^{\circ}+65^{\circ}=180^{\circ}\), if we consider the appropriate transversal and lines, we can find parallel lines. Let's assume the transversal intersects \(x\) and \(z\). The \(115^{\circ}\) and \(65^{\circ}\) angles are same - side interior angles. So \(x\parallel z\).

Answer:

In the first diagram, \(a\parallel c\). In the second diagram, \(x\parallel z\).