Question

1. determine which lines, if any, are parallel. 6. determine which lines are parallel, if any

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 the first set of lines

In the first diagram, the 124 - degree angles are corresponding angles. Since they are equal, line \(a\) is parallel to line \(c\).

Step3: Analyze the second set of lines

In the second diagram, the 27 - degree angles are corresponding angles. Also, \(153^{\circ}+27^{\circ}=180^{\circ}\) (same - side interior angles are supplementary). So, line \(a\) is parallel to line \(c\), and line \(b\) is parallel to line \(d\).

Answer:

In the first diagram: line \(a\) is parallel to line \(c\). In the second diagram: line \(a\) is parallel to line \(c\), and line \(b\) is parallel to line \(d\).