Question

lines a, b, c, and d intersect as shown. which pair of lines are parallel? a. a and b b. a and c c. c and d d. b and d

Explanation:

Step1: Recall parallel - line angle properties

If two lines are parallel, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Analyze angles related to each pair of lines

For lines \(a\) and \(b\): There are no obvious equal corresponding, alternate - interior or supplementary same - side interior angles.
For lines \(a\) and \(c\): Consider the angles formed. The angles don't satisfy the parallel - line angle relationships.
For lines \(c\) and \(d\): The angles formed don't meet the parallel - line angle criteria.
For lines \(b\) and \(d\): The vertical angles at the intersection of \(b\) and \(c\) and \(d\) and \(c\) are \(95^{\circ}\). Since vertical angles are equal, and these are corresponding angles for lines \(b\) and \(d\) with respect to the transversal \(c\), lines \(b\) and \(d\) are parallel.

Answer:

D. b and d