Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle ihe = 46^{circ}$, what is $mangle ghe$?

Explanation:

Step1: Recall angle - addition property

$\angle IHE+\angle GHE = 180^{\circ}$ (linear - pair of angles).

Step2: Solve for $\angle GHE$

Given $\angle IHE = 46^{\circ}$, then $\angle GHE=180^{\circ}-\angle IHE$.
Substitute $\angle IHE = 46^{\circ}$ into the formula: $\angle GHE = 180 - 46$.
$\angle GHE=134^{\circ}$.

Answer:

$134$