Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle feh = 112^{circ}$, what is $mangle ghe$?

Explanation:

Step1: Identify angle - relationship

$\angle FEH$ and $\angle GHE$ are supplementary angles since $\overleftrightarrow{DF}$ and $\overleftrightarrow{GI}$ are parallel lines and $JC$ is a transversal.

Step2: Use supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. So, $m\angle FEH + m\angle GHE=180^{\circ}$.

Step3: Solve for $m\angle GHE$

Given $m\angle FEH = 112^{\circ}$, then $m\angle GHE=180^{\circ}-m\angle FEH$. Substitute $m\angle FEH = 112^{\circ}$ into the equation: $m\angle GHE = 180 - 112=68^{\circ}$.

Answer:

$68$