Question

with the given information, can it be determined that m||n? write yes or no. if yes, state the theorem used. m∠1 + m∠2 = 180°. choose the correct answer below. a. yes, the lines are parallel by the converse of the corresponding angles theorem. b. yes, the lines are parallel by the converse of the same - side interior angles postulate. c. yes, the lines are parallel by the converse of the alternate exterior angles theorem. d. yes, the lines are parallel by the converse of the alternate interior angles theorem.

Explanation:

Step1: Recall angle - line relationship

Same - side interior angles are two angles that are on the same side of a transversal and between two lines. If the sum of two same - side interior angles is 180°, the two lines are parallel.

Step2: Analyze given angles

Given that \(m\angle1 + m\angle2=180^{\circ}\), if \(\angle1\) and \(\angle2\) are same - side interior angles, by the Converse of the Same - Side Interior Angles Postulate, the two lines \(m\) and \(n\) are parallel.

Answer:

B. Yes, the lines are parallel by the Converse of the Same - Side Interior Angles Postulate