#15 Which lines are parallel if m∠1 + m∠2 = 180? Justify your answer.

Question

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j || k by the converse of the Same-Side Interior Angles Theorem.
j || k by the converse of the Alternate Interior Angles Theorem.
g || h by the converse of the Alternate Interior Angles Theorem.
g || h by the converse of the Same-Side Interior Angles Theorem.

Answer 1

g || h by the converse of the Same-Side Interior Angles Theorem.

This theorem states that if two lines are cut by a transversal and the same-side interior angles add up to 180 degrees, then the lines are parallel. Since m∠1 + m∠2 = 180 in this scenario, lines g and h must be parallel.