Question

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look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 68^{circ}$, what is $mangle feh$?

Explanation:

Step1: Identify angle - relationship

$\angle DEH$ and $\angle FEH$ are a linear - pair of angles.

Step2: Recall linear - pair property

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

Step3: Solve for $\angle FEH$

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

Answer:

$112$