Question

look at this diagram: if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle hgj = 59^{circ}$, what is $mangle fgj$?

Explanation:

Step1: Identify angle - relationship

$\angle HGJ$ and $\angle FGJ$ are supplementary angles.

Step2: Use supplementary - angle property

Supplementary angles add up to $180^{\circ}$. So $m\angle FGJ=180^{\circ}-m\angle HGJ$.

Step3: Substitute the given value

Given $m\angle HGJ = 59^{\circ}$, then $m\angle FGJ=180 - 59$.
$m\angle FGJ = 121^{\circ}$

Answer:

$121$