Question

if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle dec = 111.9^{circ}$, what is $mangle ghj$?

Explanation:

Step1: Identify angle - relationship

$\angle DEC$ and $\angle GHE$ are corresponding angles since $\overleftrightarrow{DF}$ and $\overleftrightarrow{GI}$ are parallel lines. So, $m\angle GHE=m\angle DEC = 111.9^{\circ}$.

Step2: Note vertical - angle property

$\angle GHJ$ and $\angle GHE$ are a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle GHJ = 180^{\circ}-m\angle GHE$.

Step3: Calculate $m\angle GHJ$

$m\angle GHJ=180 - 111.9=68.1^{\circ}$

Answer:

$68.1$