Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle utw = 51^{circ}$, what is $mangle utr$?

Explanation:

Step1: Recall linear - pair property

Angles $\angle UTW$ and $\angle UTR$ form a linear - pair.

Step2: Use linear - pair angle sum

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

Step3: Solve for $m\angle UTR$

Given $m\angle UTW = 51^{\circ}$, we substitute into the equation: $m\angle UTR=180^{\circ}-m\angle UTW$. Then $m\angle UTR = 180 - 51=129^{\circ}$.

Answer:

$129$