Question

look at this diagram: if rt and uw are parallel lines and m∠wvs = 62°, what is m∠rsv?

Explanation:

Step1: Identify angle - relationship

$\angle WVS$ and $\angle RSV$ are supplementary angles since $\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$ and they are same - side interior angles.

Step2: Use the supplementary - angle property

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

Step3: Solve for $m\angle RSV$

Given $m\angle WVS = 62^{\circ}$, then $m\angle RSV=180^{\circ}-m\angle WVS$. Substitute $m\angle WVS = 62^{\circ}$ into the equation: $m\angle RSV = 180 - 62=118^{\circ}$.

Answer:

$118$