Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle dec = 110^{circ}$, what is $mangle deh$?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the measures of two angles in a linear pair is 180°. $\angle DEC$ and $\angle DEH$ form a linear pair.
So, $m\angle DEC + m\angle DEH=180^{\circ}$.

Step2: Solve for $m\angle DEH$

Given $m\angle DEC = 110^{\circ}$, we substitute into the equation: $m\angle DEH=180^{\circ}-m\angle DEC$.
$m\angle DEH = 180 - 110$.
$m\angle DEH=70^{\circ}$.

Answer:

$70$