Question

look at this diagram! if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle vwi = 117^{circ}$, what is $mangle xwi$?

Explanation:

Step1: Identify angle - relationship

$\angle VWI$ and $\angle XWI$ are supplementary angles since they form a linear - pair (two adjacent angles whose non - common sides are opposite rays).

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle VWI = 117^{\circ}$ and $m\angle XWI=x$. Then $m\angle VWI + m\angle XWI=180^{\circ}$, so $x = 180^{\circ}-m\angle VWI$.

Step3: Calculate the angle measure

Substitute $m\angle VWI = 117^{\circ}$ into the formula: $x=180 - 117=63^{\circ}$.

Answer:

$63$