Question

look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarrow{qs}$ are parallel lines and $mangle pom = 127^{circ}$, what is $mangle sro$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle POM$ and $\angle NOM$ form a linear - pair. Since $\angle POM = 127^{\circ}$, and $\angle POM+\angle NOM = 180^{\circ}$, then $\angle NOM=180 - 127=53^{\circ}$. Also, $\angle POM$ and $\angle NOR$ are vertical angles, so $\angle NOR = 127^{\circ}$.

Step2: Use the property of corresponding angles

Because $\overleftrightarrow{NP}$ and $\overleftrightarrow{QS}$ are parallel lines, $\angle SRO$ and $\angle NOR$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent. So $\angle SRO=\angle NOR$.

Answer:

$127$