Question

look at this diagram: if (overrightarrow{rt}) and (overrightarrow{uw}) are parallel lines and (mangle rsv = 134^{circ}), what is (mangle wvs)?

Explanation:

Step1: Identify angle - relationship

Since $\overleftrightarrow{RT}$ and $\overleftrightarrow{UW}$ are parallel lines and $\angle RSV$ and $\angle WVS$ are same - side interior angles.

Step2: Apply property of same - side interior angles

Same - side interior angles of parallel lines are supplementary, so $m\angle RSV+m\angle WVS = 180^{\circ}$.

Step3: Solve for $m\angle WVS$

Given $m\angle RSV = 134^{\circ}$, then $m\angle WVS=180^{\circ}-m\angle RSV$. Substitute $m\angle RSV = 134^{\circ}$ into the equation: $m\angle WVS = 180 - 134=46^{\circ}$.

Answer:

$46$