Question

look at this diagram: if $overleftrightarrow{jl}$ and $overleftrightarrow{mo}$ are parallel lines and $mangle lkn = 42^{circ}$, what is $mangle jkn$?

Explanation:

Step1: Identify angle - relationship

$\angle LKN$ and $\angle JKN$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle JKN=x$. We know that $m\angle LKN + x=180^{\circ}$. Given $m\angle LKN = 42^{\circ}$, then $x = 180^{\circ}-42^{\circ}$.
$x=138^{\circ}$

Answer:

$138$