Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle wvs = 123^{circ}$, what is $mangle uvs$?

Explanation:

Step1: Identify angle - relationship

$\angle WVS$ and $\angle UVS$ are supplementary angles (linear - pair).

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle WVS = 123^{\circ}$ and $m\angle UVS=x$. Then $x + 123^{\circ}=180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}- 123^{\circ}=57^{\circ}$.

Answer:

$57$