Question

look at this diagram: if rt and uw are parallel lines and m∠wvs = 122°, what is m∠uvx?

Explanation:

Step1: Identify angle - relationship

$\angle WVS$ and $\angle WSR$ are supplementary angles since they are same - side interior angles formed by parallel lines $\overleftrightarrow{RT}$ and $\overleftrightarrow{UW}$ cut by transversal $\overleftrightarrow{XQ}$.

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Given $m\angle WVS = 122^{\circ}$, let $m\angle WSR=x$. Then $m\angle WVS+x = 180^{\circ}$.

Step3: Solve for the angle

$x=180^{\circ}-m\angle WVS$. Substitute $m\angle WVS = 122^{\circ}$ into the equation: $x = 180 - 122=58^{\circ}$.

Answer:

$58^{\circ}$