Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle stq = 117^{circ}$, what is $mangle rqt$?

Explanation:

Step1: Identify angle - relationship

$\angle STQ$ and $\angle RQT$ are same - side interior angles.

Step2: Recall property of same - side interior angles

When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., their sum is $180^{\circ}$. So $m\angle STQ + m\angle RQT=180^{\circ}$.

Step3: Solve for $m\angle RQT$

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

Answer:

$63$