Question

look at this diagram: if $overleftrightarrow{np}$ and $overleftrightarrow{qs}$ are parallel lines and $mangle{sro}=67^{circ}$, what is $mangle{qro}$?

Explanation:

Step1: Recall angle - addition property

Angles $\angle SRO$ and $\angle QRO$ are a linear - pair.

Step2: Use linear - pair angle relationship

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

Step3: Solve for $m\angle QRO$

Given $m\angle SRO = 67^{\circ}$, then $m\angle QRO=180^{\circ}-m\angle SRO$. Substitute $m\angle SRO = 67^{\circ}$ into the equation: $m\angle QRO = 180 - 67=113^{\circ}$.

Answer:

$113$