Question

look at this diagram: if $overleftrightarrow{km}$ and $overleftrightarrow{np}$ are parallel lines and $mangle poq = 122^{circ}$, what is $mangle noq$?

Explanation:

Step1: Recall linear - pair property

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

Step2: Solve for $m\angle NOQ$

Given $m\angle POQ = 122^{\circ}$, we substitute into the equation:
$m\angle NOQ=180^{\circ}-m\angle POQ$.
$m\angle NOQ = 180 - 122$.
$m\angle NOQ = 58^{\circ}$.

Answer:

$58^{\circ}$