Question

1. determine which lines, if any, are parallel

Explanation:

Step1: Recall parallel - line 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 angle relationships

The angle of \(51^{\circ}\) and the angle of \(129^{\circ}\) are supplementary (\(51^{\circ}+ 129^{\circ}=180^{\circ}\)). These are same - side interior angles formed by lines \(a\) and \(b\) with a transversal.

Step3: Determine parallel lines

Since the same - side interior angles between lines \(a\) and \(b\) are supplementary, lines \(a\) and \(b\) are parallel. The \(52^{\circ}\) angles are corresponding angles for lines \(c\) and \(d\), so lines \(c\) and \(d\) are parallel.

Answer:

Lines \(a\) and \(b\) are parallel, and lines \(c\) and \(d\) are parallel.