Question

look at this diagram: if (overrightarrow{rt}) and (overrightarrow{uw}) are parallel lines and (mangle wvs = 136^{circ}), what is (mangle rsv)?

Explanation:

Step1: Identify angle - relationship

$\angle WVS$ and $\angle RSV$ are supplementary angles since $\overrightarrow{RT}$ and $\overrightarrow{UW}$ are parallel lines and $\overrightarrow{QX}$ is a transversal.

Step2: Use the supplementary - angle formula

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

Step3: Substitute the given value

Given $m\angle WVS = 136^{\circ}$, we have $x+136^{\circ}=180^{\circ}$. Solving for $x$, we get $x = 180^{\circ}-136^{\circ}$.

Step4: Calculate the angle measure

$x = 44^{\circ}$.

Answer:

$44^{\circ}$