Question

look at this diagram: if $overleftrightarrow{jl}$ and $overleftrightarrow{mo}$ are parallel lines and $mangle mnk = 138^{circ}$, what is $mangle onk$?

Explanation:

Step1: Recall linear - pair property

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

Step2: Solve for $m\angle ONK$

Given $m\angle MNK = 138^{\circ}$, we substitute into the equation:
$m\angle ONK=180^{\circ}-m\angle MNK$.
$m\angle ONK = 180 - 138$.
$m\angle ONK = 42^{\circ}$.

Answer:

$42$