Question

are lines l and m parallel? explain how you know.

Explanation:

Step1: Find the supplementary angle of \(146^{\circ}\)

The supplementary angle of \(146^{\circ}\) is \(180^{\circ}- 146^{\circ}=34^{\circ}\)

Step2: Check the relationship between the angles

Since the supplementary angle of \(146^{\circ}\) (\(34^{\circ}\)) is equal to the given \(34^{\circ}\) angle, by the converse of the corresponding angles postulate, lines \(l\) and \(m\) are parallel.

Answer:

Lines \(l\) and \(m\) are parallel. The supplementary angle of \(146^{\circ}\) is \(34^{\circ}\), which is equal to the other given angle. By the converse of the corresponding angles postulate, if two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel.