Question

look at this diagram: if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle fge = 120.7^{circ}$, what is $mangle hge$?

Explanation:

Step1: Identify angle - relationship

$\angle FGE$ and $\angle HGE$ are supplementary angles.

Step2: Use supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle HGE=x$. Then $m\angle FGE + x=180^{\circ}$. Given $m\angle FGE = 120.7^{\circ}$, we have $x = 180^{\circ}-120.7^{\circ}$.

Step3: Calculate the angle measure

$x=180 - 120.7=59.3^{\circ}$.

Answer:

$59.3$