Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 134^{circ}$, what is $mangle feh$?

Explanation:

Step1: Recall linear - pair property

$\angle DEH$ and $\angle FEH$ form a linear - pair. 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 $m\angle DEH = 134^{\circ}$. Substitute this value into the equation $m\angle DEH + m\angle FEH = 180^{\circ}$. Then $m\angle FEH=180^{\circ}-m\angle DEH$.
$m\angle FEH = 180 - 134=46^{\circ}$

Answer:

$46$