Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle fec = 121^{circ}$, what is $mangle feh$?

Explanation:

Step1: Recall linear - pair property

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

Step2: Solve for $m\angle FEH$

Given $m\angle FEC = 121^{\circ}$, we substitute into the equation: $m\angle FEH=180^{\circ}-m\angle FEC$.
$m\angle FEH = 180 - 121=59^{\circ}$.

Answer:

$59$