Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle nmk = 137^{circ}$, what is $mangle lmk$?

Explanation:

Step1: Identify angle - relationship

$\angle NMK$ and $\angle LMK$ are a linear - pair of angles.

Step2: Use linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. So, $m\angle NMK+m\angle LMK = 180^{\circ}$.

Step3: Solve for $m\angle LMK$

Given $m\angle NMK = 137^{\circ}$, then $m\angle LMK=180^{\circ}-m\angle NMK$. Substitute $m\angle NMK = 137^{\circ}$ into the equation: $m\angle LMK = 180 - 137=43^{\circ}$.

Answer:

$43$