Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle xwy = 56^{circ}$, what is $mangle vwt$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle XWY$ and $\angle VWU$ are vertical angles. Vertical angles are equal. So $m\angle VWU=m\angle XWY = 56^{\circ}$.

Step2: Use linear - pair property

$\angle VWU$ and $\angle VWT$ form a linear - pair. A linear - pair of angles is supplementary, that is $m\angle VWU + m\angle VWT=180^{\circ}$.

Step3: Solve for $m\angle VWT$

$m\angle VWT=180^{\circ}-m\angle VWU$. Substitute $m\angle VWU = 56^{\circ}$ into the equation. So $m\angle VWT=180 - 56=124^{\circ}$.

Answer:

$124^{\circ}$