Question

look at this diagram: if $overleftrightarrow{qs}$ and $overleftrightarrow{tv}$ are parallel lines and $mangle sru = 56^{circ}$, what is $mangle tur$?

Explanation:

Step1: Identify angle - relationship

$\angle SRU$ and $\angle TUR$ are supplementary angles since $\overleftrightarrow{QS}$ and $\overleftrightarrow{TV}$ are parallel lines and $\overleftrightarrow{WP}$ is a transversal.

Step2: Use supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. So, $m\angle TUR=180^{\circ}-m\angle SRU$.

Step3: Substitute the given value

Given $m\angle SRU = 56^{\circ}$, then $m\angle TUR=180 - 56$.
$m\angle TUR = 124^{\circ}$

Answer:

$124$