Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle ihj = 137^{circ}$, what is $mangle ghe$?

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning their sum is 180°. $\angle IHJ$ and $\angle GHE$ form a linear - pair.
Let $m\angle GHE=x$. Then $m\angle IHJ + x=180^{\circ}$.

Step2: Substitute the given angle value

We know that $m\angle IHJ = 137^{\circ}$. Substituting into the equation $137^{\circ}+x = 180^{\circ}$.
Solve for $x$: $x=180^{\circ}-137^{\circ}$.
$x = 43^{\circ}$.

Answer:

$43$