Question

look at this diagram: if (overrightarrow{jl}) and (overrightarrow{mo}) are parallel lines and (mangle jkn = 134^{circ}), what is (mangle lkn?)

Explanation:

Step1: Recall angle - addition postulate

$\angle JKN$ and $\angle LKN$ are adjacent angles that form a linear - pair. A linear - pair of angles is supplementary, meaning the sum of their measures is $180^{\circ}$.
Let $m\angle JKN = 134^{\circ}$ and $m\angle LKN=x$. Then $m\angle JKN + m\angle LKN=180^{\circ}$.

Step2: Solve for $m\angle LKN$

We have the equation $134^{\circ}+x = 180^{\circ}$.
Subtract $134^{\circ}$ from both sides of the equation: $x=180^{\circ}-134^{\circ}$.
$x = 46^{\circ}$.

Answer:

$46$