Question

look at this diagram: if $overleftrightarrow{qs}$ and $overleftrightarrow{tv}$ are parallel lines and $mangle vuw = 122^{circ}$, what is $mangle tuw$?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the angles in a linear pair is 180°. $\angle VUW$ and $\angle TUW$ form a linear pair.

Step2: Set up the equation

Let $m\angle VUW = 122^{\circ}$ and $m\angle TUW=x$. Then $m\angle VUW + m\angle TUW=180^{\circ}$, so $122^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

Subtract 122° from both sides of the equation: $x=180^{\circ}- 122^{\circ}$.
$x = 58^{\circ}$

Answer:

$58$