Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle vwy = 64.3^{circ}$, what is $mangle xwy$?

Explanation:

Step1: Recall angle - addition property

Angles $\angle VWY$ and $\angle XWY$ are adjacent angles that form a straight - line. The sum of adjacent angles on a straight - line is $180^{\circ}$.
So, $m\angle VWY + m\angle XWY=180^{\circ}$.

Step2: Solve for $m\angle XWY$

We know that $m\angle VWY = 64.3^{\circ}$. Rearranging the equation from Step 1 gives $m\angle XWY=180^{\circ}-m\angle VWY$.
Substitute $m\angle VWY = 64.3^{\circ}$ into the equation: $m\angle XWY = 180 - 64.3=115.7^{\circ}$.

Answer:

$115.7$