Question

look at this diagram:
if \\( \overleftrightarrow{ln} \\) and \\( \overleftrightarrow{oq} \\) are parallel lines and \\( m\angle opr = 116^\circ \\), what is \\( m\angle nmk \\)?

Explanation:

Step1: Identify vertical angle

$\angle OPR$ and $\angle QPM$ are vertical angles, so $m\angle QPM = m\angle OPR = 116^\circ$.

Step2: Use parallel line property

Since $\overleftrightarrow{LN} \parallel \overleftrightarrow{OQ}$, $\angle QPM$ and $\angle NMK$ are corresponding angles, so $m\angle NMK = m\angle QPM$.

Answer:

$116^\circ$