Question

which two lines are parallel? (hint: use the angle relationships not whether they look parallel!) lines m and p lines m and n lines n and p

Explanation:

Step1: Find the measure of the angle adjacent to \( 112^{\circ} \)

The adjacent angle is \( 180^{\circ}-112^{\circ} = 68^{\circ} \) (supplementary angles).

Step2: Check the relationship with the other angles

The angle of \( 68^{\circ} \) (from step 1) and the \( 107^{\circ} \) - related angles (if we consider the transversal - line relationships). But for lines \( M \) and \( P \), using the property that if the corresponding or alternate - interior angles (after calculating the adjacent angle to \( 112^{\circ} \)) satisfy the parallel - line angle criteria. The angle adjacent to \( 112^{\circ}(68^{\circ}) \) and the angle related to line \( P \) (by vertical or other angle - chasing) follow the rule that when a transversal intersects two lines, if the corresponding angles are equal, the lines are parallel. Here, after proper angle - chasing (using supplementary and vertical angle properties), lines \( M \) and \( P \) meet the parallel - line angle conditions. Lines \( M \) and \( N \) and \( N \) and \( P \) do not satisfy the angle - based parallel - line criteria (e.g., if we assume a transversal, the angle sums or equalities for parallel lines are not met for \( M - N \) and \( N - P \) pairs).

Answer:

Lines \( M \) and \( P \)