Question

if (overrightarrow{rt}) and (overrightarrow{uw}) are parallel lines and (mangle wvs = 59^{circ}), what is (mangle uvs)?

Explanation:

Step1: Recall angle - relationship

$\angle WVS$ and $\angle UVS$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. So, $m\angle WVS + m\angle UVS=180^{\circ}$.

Step3: Solve for $m\angle UVS$

Given $m\angle WVS = 59^{\circ}$, we substitute into the formula: $m\angle UVS=180^{\circ}-m\angle WVS$. Then $m\angle UVS = 180 - 59=121^{\circ}$.

Answer:

$121$