Question

which lines are parallel if m∠1 + m∠2 = 180? justify your answer. o j || k, by the converse of the alternate interior angles theorem o g || h, by the converse of the same - side interior angles postulate o g || h, by the converse of the alternate interior angles theorem o j || k, by the converse of the same - side interior angles postulate

Explanation:

Step1: Identify angle - type relationship

$\angle1$ and $\angle2$ are same - side interior angles formed by lines $g$, $h$ and transversal $k$.

Step2: Apply relevant theorem

The Converse of 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 two lines are parallel. Since $m\angle1 + m\angle2=180$, lines $g$ and $h$ are parallel.

Answer:

$g\parallel h$, by the Converse of the Same - Side Interior Angles Postulate