Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle rqs = 67^{circ}$, what is $mangle pqs?$

Explanation:

Step1: Recall angle - addition property

$\angle PQS$ and $\angle RQS$ form a linear - pair. A linear - pair of angles are supplementary, meaning the sum of their measures is $180^{\circ}$.
So, $m\angle PQS + m\angle RQS=180^{\circ}$.

Step2: Solve for $m\angle PQS$

We know that $m\angle RQS = 67^{\circ}$. Substitute this value into the equation $m\angle PQS+67^{\circ}=180^{\circ}$.
Then $m\angle PQS=180^{\circ}-67^{\circ}$.
$m\angle PQS = 113^{\circ}$.

Answer:

$113$