Question

look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarrow{qs}$ are parallel lines and $mangle{sro}=65^{circ}$, what is $mangle{qro}$?

Explanation:

Step1: Recall linear - pair property

$\angle SRO$ and $\angle QRO$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.
So, $m\angle SRO + m\angle QRO=180^{\circ}$.

Step2: Solve for $m\angle QRO$

Given $m\angle SRO = 65^{\circ}$, we substitute into the equation: $m\angle QRO=180^{\circ}-m\angle SRO$.
$m\angle QRO = 180 - 65$.
$m\angle QRO=115^{\circ}$.

Answer:

$115$