Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle utv = 138^{circ}$, what is $mangle rqt$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle UTV$ and $\angle STQ$ are vertical angles. So, $m\angle STQ=m\angle UTV = 138^{\circ}$

Step2: Use corresponding - angle property

Since $\overleftrightarrow{PR}$ and $\overleftrightarrow{SU}$ are parallel lines, $\angle RQT$ and $\angle STQ$ are corresponding angles. So, $m\angle RQT=m\angle STQ$

Answer:

$138$