Question

if $overleftrightarrow{ik}$ and $overleftrightarrow{ln}$ are parallel lines and $mangle nmj = 58^{circ}$, what is $mangle ijm$?

Explanation:

Step1: Identify angle - relationship

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

Step2: Apply property of parallel lines

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

Answer:

$58^{\circ}$