Question

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

Explanation:

Step1: Recall parallel - line angle rules

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 problem 8

For the first set of lines in problem 8:
The angle between line \(l\) and the transversal is \(115^{\circ}\), and the angle between line \(m\) and the transversal is \(115^{\circ}\). These are corresponding angles. Since the corresponding angles are equal (\(115^{\circ}=115^{\circ}\)), lines \(l\) and \(m\) are parallel. Also, the angle between line \(n\) and the transversal is \(60^{\circ}\), and the other \(60^{\circ}\) angle is also a corresponding angle, so lines \(n\) and \(p\) are parallel.

Step3: Analyze problem 9

For the second set of lines in problem 9:
There are no equal corresponding angles, no equal alternate - interior angles, and no supplementary same - side interior angles among the lines \(a\), \(b\), \(c\), \(d\), and \(e\). So, no lines are parallel in problem 9.

Answer:

In problem 8, lines \(l\) and \(m\) are parallel, and lines \(n\) and \(p\) are parallel. In problem 9, no lines are parallel.