Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle utw = 140^{circ}$, what is $mangle stw$?

Explanation:

Step1: Identify angle - relationship

$\angle UTW$ and $\angle STW$ are supplementary angles.

Step2: Use supplementary - angle formula

Supplementary angles add up to $180^{\circ}$. Let $m\angle STW = x$. Then $m\angle UTW+x = 180^{\circ}$. Given $m\angle UTW = 140^{\circ}$, we have $140^{\circ}+x=180^{\circ}$.

Step3: Solve for $x$

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

Answer:

$40$