Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle utw = 66^{circ}$, what is $mangle vwt$?

Explanation:

Step1: Identify angle - relationship

$\angle UTW$ and $\angle VWT$ are alternate - interior angles.

Step2: Apply alternate - interior angles theorem

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overrightarrow{SU}$ and $\overrightarrow{VX}$ are parallel and $YR$ is the transversal, $m\angle VWT=m\angle UTW$.

Answer:

$66^{\circ}$