Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle stw = 67.7^{circ}$, what is $mangle utw$?

Explanation:

Step1: Recall linear - pair property

Angles $\angle STW$ and $\angle UTW$ form a linear - pair. The sum of the measures of angles in a linear - pair is $180^{\circ}$.
So, $m\angle STW + m\angle UTW=180^{\circ}$.

Step2: Solve for $m\angle UTW$

We know that $m\angle STW = 67.7^{\circ}$. Substitute this value into the equation $m\angle STW + m\angle UTW = 180^{\circ}$.
$m\angle UTW=180^{\circ}-m\angle STW$.
$m\angle UTW = 180 - 67.7=112.3^{\circ}$

Answer:

$112.3$