Question

look at this diagram: if $overline{su}$ and $overline{vx}$ are parallel lines and $mangle xwt = 122^{circ}$, what is $mangle vwt$?

Explanation:

Step1: Identify angle - relationship

$\angle XWT$ and $\angle VWT$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle property

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle VWT=x$. We know that $m\angle XWT = 122^{\circ}$ and $m\angle XWT+m\angle VWT=180^{\circ}$. So, $x + 122^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Subtract $122^{\circ}$ from both sides of the equation: $x=180^{\circ}-122^{\circ}$.
$x = 58^{\circ}$

Answer:

$58$