Question

look at this diagram: if (overline{rt}) and (overline{uw}) are parallel lines and (mangle wvs = 118^{circ}), what is (mangle tsv?)

Explanation:

Step1: Identify angle - relationship

$\angle WVS$ and $\angle TSV$ are supplementary angles since $\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$ and they are same - side interior angles.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle TSV = x$. We know that $m\angle WVS=118^{\circ}$, and $m\angle WVS + x=180^{\circ}$. So $x = 180^{\circ}-m\angle WVS$.

Step3: Calculate the angle measure

Substitute $m\angle WVS = 118^{\circ}$ into the formula: $x=180 - 118=62^{\circ}$.

Answer:

$62$