Question

which lines are parallel if (mangle1 + mangle2 = 180)? justify your answer.
(g parallel h), by the converse of the alternate interior angles theorem
(g parallel h), by the converse of the same - side interior angles postulate
(j parallel k), by the converse of the alternate interior angles theorem
(j parallel k), by the converse of the same - side interior angles postulate

Explanation:

Step1: Identify angle - type

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

Step2: Apply the converse 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 $j$ and $k$ are parallel by the Converse of the Same - Side Interior Angles Postulate.

Answer:

$j\parallel k$, by the Converse of the Same - Side Interior Angles Postulate