Question

look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle{lmo}=58^{circ}), what is (mangle{nmo}?)

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning they add up to 180°. $\angle LMO$ and $\angle NMO$ form a linear - pair.

Step2: Set up the equation

Let $m\angle LMO = 58^{\circ}$ and $m\angle NMO=x$. Then $m\angle LMO + m\angle NMO=180^{\circ}$, so $58^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-58^{\circ}$.
$x = 122^{\circ}$.

Answer:

$122$