Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 69.6^{circ}$, what is $mangle feh$?

Explanation:

Step1: Recall angle - addition postulate

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

Step2: Solve for $m\angle FEH$

We know that $m\angle DEH = 69.6^{\circ}$. Rearranging the equation $m\angle DEH + m\angle FEH = 180^{\circ}$ gives $m\angle FEH=180^{\circ}-m\angle DEH$. Substitute $m\angle DEH = 69.6^{\circ}$ into the equation: $m\angle FEH = 180 - 69.6=110.4^{\circ}$.

Answer:

$110.4$