Question

which lines are parallel if ( mangle1 + mangle2 = 180 )? justify your answer.

( \bigcirc gparallel h ), by the converse of the same - side interior angles postulate
( \bigcirc jparallel k ), by the converse of the alternate interior angles theorem
( \bigcirc gparallel h ), by the converse of the alternate interior angles theorem
( \bigcirc jparallel k ), by the converse of the same - side interior angles postulate

Explanation:

The Same - Side Interior Angles Postulate states that if two lines are cut by a transversal and the same - side interior angles are supplementary (\(m\angle1 + m\angle2=180^{\circ}\)), then the two lines are parallel. In this case, lines \(j\) and \(k\) are cut by a transversal (line \(h\)), and \(\angle1\) and \(\angle2\) are same - side interior angles. Since \(m\angle1 + m\angle2 = 180\), by the Converse of the Same - Side Interior Angles Postulate, \(j\parallel k\).

Answer:

\(j\parallel k\), by the Converse of the Same - Side Interior Angles Postulate.