Question

look at this diagram: if \\( \overleftrightarrow { n p } \\) and \\( \overleftrightarrow { q s } \\) are parallel lines and \\( m \angle s r o = 51 ^ { \circ } \\), what is \\( m \angle n o m \\)?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle SRO$ and $\angle MRO$ are vertical angles. So, $m\angle MRO = 51^{\circ}$.

Step2: Use linear - pair relationship

$\angle MRO$ and $\angle NOM$ are supplementary (linear pair). The sum of angles in a linear pair is $180^{\circ}$.
So, $m\angle NOM=180^{\circ}-m\angle MRO$.
Substitute $m\angle MRO = 51^{\circ}$ into the formula: $m\angle NOM = 180^{\circ}-51^{\circ}$.

Answer:

$129$