Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle stw = 114^{circ}$, what is $mangle xwt$?

Explanation:

Step1: Identify angle - relationship

$\angle STW$ and $\angle XWT$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$ are parallel and $\angle STW$ and $\angle XWT$ are alternate - interior angles formed by the transversal $\overleftrightarrow{YR}$, then $m\angle XWT=m\angle STW$.

Answer:

$114^{\circ}$