Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle xwy = 40^{circ}$, what is $mangle str$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle XWY$ and $\angle SWT$ are vertical angles. Vertical angles are equal, so $m\angle SWT=m\angle XWY = 40^{\circ}$.

Step2: Identify corresponding - angle relationship

Since $\overleftrightarrow{SU}$ and $\overleftrightarrow{VX}$ are parallel lines, $\angle SWT$ and $\angle STR$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle STR=m\angle SWT$.

Answer:

$40$