Question

if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle uvs = 54^{circ}$, what is $mangle tsv$?

Explanation:

Step1: Recall angle - addition property

The sum of $\angle UVS$ and $\angle TSV$ is $180^{\circ}$ since they form a linear - pair of angles (two adjacent angles whose non - common sides are opposite rays).
Let $m\angle UVS = 54^{\circ}$ and $m\angle TSV=x$. Then $\angle UVS+\angle TSV = 180^{\circ}$.

Step2: Solve for $x$

We have the equation $54^{\circ}+x = 180^{\circ}$.
Subtract $54^{\circ}$ from both sides of the equation: $x=180^{\circ}- 54^{\circ}$.
$x = 126^{\circ}$.

Answer:

$126$