Question

look at this diagram: if $overleftrightarrow{qs}$ and $overleftrightarrow{tv}$ are parallel lines and $mangle sru = 140^{circ}$, what is $mangle vur?$

Explanation:

Step1: Identify angle - relationship

$\angle SRU$ and $\angle VUR$ are supplementary angles since $\overleftrightarrow{QS}$ and $\overleftrightarrow{TV}$ are parallel lines and they are same - side interior angles.

Step2: Use the supplementary - angle formula

Let $m\angle SRU = 140^{\circ}$ and $m\angle VUR=x$. The sum of supplementary angles is $180^{\circ}$, so $m\angle SRU + m\angle VUR=180^{\circ}$, which gives $140^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}- 140^{\circ}=40^{\circ}$

Answer:

$40$