Question

look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle nmj = 68^{circ}), what is (mangle ijm?)

Explanation:

Step1: Identify angle - type relationship

$\angle NMJ$ and $\angle IJM$ are alternate - interior angles.

Step2: Apply the property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{IK}$ and $\overleftrightarrow{LN}$ are parallel and $OH$ is the transversal, $m\angle IJM=m\angle NMJ$.

Answer:

$68$