Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle str = 57^{circ}$, what is $mangle utr$?

Explanation:

Step1: Recall angle - sum property

$\angle STR$ and $\angle UTR$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle STR + m\angle UTR=180^{\circ}$.

Step2: Solve for $m\angle UTR$

Given $m\angle STR = 57^{\circ}$, we substitute into the equation: $m\angle UTR=180^{\circ}-m\angle STR$. Then $m\angle UTR = 180 - 57$.

Answer:

$123$