Question

in this figure, lines a, b, c, d, and e intersect as shown. based on the angle measures, which pair of lines is parallel? note: the figure is not drawn to scale.

Explanation:

Step1: Recall parallel - line angle rules

If two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary (sum to 180°).

Step2: Analyze angles related to each pair of lines

For lines \(a\) and \(b\):
There are no obvious angle relationships (corresponding, alternate - interior, or same - side interior) that would indicate they are parallel.
For lines \(c\) and \(e\):
The angle adjacent to the \(151^{\circ}\) angle on line \(a\) is \(180 - 151=29^{\circ}\) (linear - pair angles). This \(29^{\circ}\) angle and the \(29^{\circ}\) angle formed by lines \(c\) and \(a\) and lines \(e\) and \(a\) are corresponding angles. Since corresponding angles are equal, lines \(c\) and \(e\) are parallel.
For lines \(c\) and \(d\):
There are no angle relationships that would indicate they are parallel.
For lines \(d\) and \(e\):
There are no angle relationships that would indicate they are parallel.

Answer:

B. \(c\) and \(e\)