Question

look at this diagram: if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle fgj = 112^{circ}$, what is $mangle kjg$?

Explanation:

Step1: Identify angle - relationship

$\angle FGJ$ and $\angle KJG$ are vertical - angles. Vertical angles are congruent.
So, $m\angle KJG=m\angle FGJ = 112^{\circ}$.

Step2: Use linear - pair property

$\angle KJG$ and $\angle KJG$ and $\angle KJG$ form a linear - pair. A linear pair of angles is supplementary, that is, their sum is $180^{\circ}$. Let $m\angle KJG = x$.
We know that $x + m\angle KJG=180^{\circ}$. Since $m\angle KJG = 112^{\circ}$, then $x=180 - 112$.
$x = 68^{\circ}$.

Answer:

$68$