Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 50.6^{circ}$, what is $mangle dec$?

Explanation:

Step1: Recall linear - pair property

$\angle DEH$ and $\angle DEC$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.
So, $m\angle DEH + m\angle DEC=180^{\circ}$.

Step2: Solve for $m\angle DEC$

We know that $m\angle DEH = 50.6^{\circ}$.
Substitute the value of $m\angle DEH$ into the equation: $m\angle DEC=180^{\circ}-m\angle DEH$.
$m\angle DEC = 180 - 50.6=129.4^{\circ}$.

Answer:

$129.4$