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 same - side interior angles postulate. b. yes, the lines are parallel by the converse of the corresponding angles theorem. 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. e. no, it cannot be determined

Explanation:

Step1: Recall parallel - line theorems

The Same - Side Interior Angles Postulate states that if two lines are cut by a transversal and the same - side interior angles are supplementary (sum to 180°), then the lines are parallel.

Step2: Analyze given angles

We are given that \(m\angle1 + m\angle2=180^{\circ}\), and \(\angle1\) and \(\angle2\) are same - side interior angles.

Answer:

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