Question

determine which lines, if any are parallel.

Explanation:

Step1: Recall parallel - line angle rules

If two lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary for parallel lines.

Step2: Analyze the given angles

We know that if two lines are parallel, the corresponding angles are congruent. Let's assume the lines are \(l_1\), \(l_2\), \(l_3\) and the transversals are \(t_1\), \(t_2\).
We see that the angle of \(120^{\circ}\) and the angle adjacent to the \(60^{\circ}\) angle (which is also \(120^{\circ}\) since they are supplementary, \(180 - 60=120^{\circ}\)) are corresponding angles.

Step3: Determine parallel lines

Lines with equal corresponding angles are parallel. So, the lines with the \(120^{\circ}\) corresponding angles are parallel.

Answer:

The lines with the \(120^{\circ}\) corresponding angles are parallel.