Question

look at this diagram: if (overrightarrow{ik}) and (overrightarrow{ln}) are parallel lines and (mangle nmj = 59^{circ}), what is (mangle ijm?)

Explanation:

Step1: Identify angle - relationship

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

Step2: Apply 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 $HO$ is the transversal, $m\angle IJM=m\angle NMJ$.

Answer:

$59$