Question

look at this diagram: if $overleftrightarrow{ce}$ and $overleftrightarrow{fh}$ are parallel lines and $mangle cdg = 128^{circ}$, what is $mangle hgd$?

Explanation:

Step1: Identify angle - relationship

$\angle CDG$ and $\angle HGD$ are same - side interior angles. When two parallel lines ($\overleftrightarrow{CE}$ and $\overleftrightarrow{FH}$) are cut by a transversal ($\overleftrightarrow{BI}$), same - side interior angles are supplementary.

Step2: Use the supplementary - angle formula

Let $m\angle CDG = 128^{\circ}$ and $m\angle HGD=x$. Since they are supplementary, $m\angle CDG + m\angle HGD=180^{\circ}$. So, $128^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}- 128^{\circ}=52^{\circ}$.

Answer:

$52$