Question

look at this diagram:
if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle tus = 58^{circ}), what is (mangle wxz)?

Explanation:

Step1: Find the measure of $\angle WXU$

Since $\overleftrightarrow{TV}$ and $\overleftrightarrow{WY}$ are parallel lines and $ZS$ is a transversal. $\angle TUS$ and $\angle WXU$ are corresponding angles. So, $m\angle WXU = m\angle TUS=58^{\circ}$ (Corresponding angles postulate: If two parallel lines are cut by a transversal, then corresponding angles are congruent).

Step2: Calculate $m\angle WXZ$

$\angle WXU$ and $\angle WXZ$ form a linear - pair. We know that the sum of angles in a linear - pair is $180^{\circ}$. Let $m\angle WXZ=x$. Then $x + 58^{\circ}=180^{\circ}$ (Linear - pair postulate: If two angles form a linear - pair, then they are supplementary).
Solve for $x$: $x=180^{\circ}- 58^{\circ}=122^{\circ}$

Answer:

$122$