Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle rqs = 60.6^{circ}$, what is $mangle pqs$?

Explanation:

Step1: Identify angle - relationship

$\angle RQS$ and $\angle PQS$ are supplementary angles.

Step2: Recall supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle PQS = x$. Then $x + m\angle RQS=180^{\circ}$.

Step3: Substitute the given value

Given $m\angle RQS = 60.6^{\circ}$, we have $x+60.6^{\circ}=180^{\circ}$.

Step4: Solve for $x$

$x = 180^{\circ}-60.6^{\circ}=119.4^{\circ}$.

Answer:

$119.4$