Question

look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarrow{qs}$ are parallel lines and $mangle qrt = 115^{circ}$, what is $mangle nom$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle QRT$ and $\angle SRO$ are vertical angles. Since vertical angles are equal, $m\angle SRO=m\angle QRT = 115^{\circ}$.

Step2: Use corresponding - angle property

$\overrightarrow{NP}$ and $\overrightarrow{QS}$ are parallel lines, and $\angle SRO$ and $\angle NOM$ are corresponding angles. For parallel lines, corresponding angles are equal. So $m\angle NOM=m\angle SRO$.

Answer:

$115$