Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle uvs = 139^{circ}$, what is $mangle tsv$?

Explanation:

Step1: Identify angle - relationship

$\angle UVS$ and $\angle TSV$ are supplementary angles since $\overleftrightarrow{RT}$ and $\overleftrightarrow{UW}$ are parallel lines and the angles are on the same - side of the transversal.

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle TSV=x$. Then $m\angle UVS + x=180^{\circ}$. Given $m\angle UVS = 139^{\circ}$, we have $x=180^{\circ}-139^{\circ}$.

Step3: Calculate the angle measure

$x = 41^{\circ}$.

Answer:

$41$