Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 125^{circ}$, what is $mangle ihe$?

Explanation:

Step1: Identify angle - relationship

$\angle DEH$ and $\angle IHE$ are same - side interior angles.
When two parallel lines ($\overleftrightarrow{DF}$ and $\overleftrightarrow{GI}$) are cut by a transversal ($\overleftrightarrow{JC}$), same - side interior angles are supplementary.

Step2: Apply the supplementary - angle formula

Let $m\angle DEH = 125^{\circ}$ and $m\angle IHE=x$.
Since they are supplementary, $m\angle DEH + m\angle IHE=180^{\circ}$.
So, $125^{\circ}+x = 180^{\circ}$.
Solve for $x$: $x=180^{\circ}- 125^{\circ}$.
$x = 55^{\circ}$.

Answer:

$55$