Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle nmp = 122^{circ}$, what is $mangle lmp$?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the measures of two angles in a linear pair is 180°. $\angle NMP$ and $\angle LMP$ form a linear pair.

Step2: Set up the equation

Let $m\angle LMP=x$. We know that $m\angle NMP + x=180^{\circ}$. Given $m\angle NMP = 122^{\circ}$, the equation becomes $122^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

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

Answer:

$58$