Question

is there enough information to conclude p || q? explain. a. no, there is not enough information. b. yes, consecutive interior angles are congruent. c. yes, consecutive interior angles are supplementary. d. yes, alternate exterior angles are supplementary.

Explanation:

Step1: Identify angle - type

The two given angles \(123^{\circ}\) and \(57^{\circ}\) are consecutive interior angles formed by the transversal intersecting lines \(p\) and \(q\).

Step2: Check angle - relationship

Calculate the sum of the two angles: \(123 + 57=180^{\circ}\). Since the sum of the consecutive interior angles is \(180^{\circ}\), they are supplementary.

Step3: Apply parallel - line theorem

If consecutive interior angles formed by a transversal intersecting two lines are supplementary, then the two lines are parallel.

Answer:

C. Yes, consecutive interior angles are supplementary.