Question

line p and line q are __________. a. parallel b. not parallel, because the two given alternate interior angles are not congruent c. not parallel, because the two given corresponding angles are not congruent d. not parallel, because the two given consecutive interior angles are not supplementary

Explanation:

Step1: Recall the property of parallel lines

If two lines are parallel and cut by a transversal, then corresponding angles are congruent, alternate - interior angles are congruent, and consecutive - interior angles are supplementary.

Step2: Analyze the given angles

The two given angles \(108^{\circ}\) and \(110^{\circ}\) are neither corresponding angles nor alternate - interior angles. They are consecutive - interior angles.
For two lines \(p\) and \(q\) cut by a transversal \(r\), if \(p\parallel q\), then the sum of consecutive - interior angles should be \(180^{\circ}\).
Calculate the sum of the two angles: \(108 + 110=218
eq180\)

Answer:

D. not parallel, because the two given consecutive interior angles are not supplementary