Question

look at this diagram: if $overleftrightarrow{ik}$ and $overleftrightarrow{ln}$ are parallel lines and $mangle nmj = 54^{circ}$, what is $mangle ijm$?

Explanation:

Step1: Identify angle - type relationship

$\overleftrightarrow{IK}$ and $\overleftrightarrow{LN}$ are parallel, and $\angle NMJ$ and $\angle IJM$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

Alternate - interior angles formed by two parallel lines and a transversal are congruent. So $m\angle IJM=m\angle NMJ$.

Answer:

$54$