Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle rqo = 63^{circ}$, what is $mangle rqt$?

Explanation:

Step1: Identify linear - pair angles

$\angle RQO$ and $\angle RQT$ form a linear - pair.

Step2: Use linear - pair property

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

Step3: Solve for $m\angle RQT$

Given $m\angle RQO = 63^{\circ}$, then $m\angle RQT=180^{\circ}-m\angle RQO$. Substitute $m\angle RQO = 63^{\circ}$ into the equation: $m\angle RQT = 180 - 63=117^{\circ}$.

Answer:

$117^{\circ}$