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

When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary (sum to 180°).

Step2: Check angles for each pair

For lines \(a\) and \(b\):

• Consider the angles formed by a transversal. Let's assume a transversal intersects \(a\) and \(b\). The angles given do not show any of the angle - relationships (corresponding, alternate - interior, or supplementary) that would indicate parallel lines.

For lines \(c\) and \(e\):

• The angles formed by a transversal do not satisfy the parallel - line angle rules.

For lines \(c\) and \(d\):

• The angles formed by a transversal do not satisfy the parallel - line angle rules.

For lines \(d\) and \(e\):

• The angle adjacent to the \(140^{\circ}\) angle on line \(d\) is \(180 - 140=40^{\circ}\) (linear - pair angles).
• The angle on line \(e\) corresponding to this \(40^{\circ}\) angle (assuming a transversal) is \(40^{\circ}\) (since \(180 - 140 = 40^{\circ}\)). Since corresponding angles are equal, lines \(d\) and \(e\) are parallel.

Answer:

D. \(d\) and \(e\)