Question

look at this diagram: if $overleftrightarrow{ce}$ and $overleftrightarrow{fh}$ are parallel lines and $mangle hgi = 132^{circ}$, what is $mangle cdg$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle HGI$ and $\angle DGF$ are vertical angles. Vertical angles are equal. So $m\angle DGF=m\angle HGI = 132^{\circ}$.

Step2: Identify supplementary - angle relationship

$\angle DGF$ and $\angle CDG$ are supplementary angles (since $\overleftrightarrow{CE}\parallel\overleftrightarrow{FH}$, and they are same - side interior angles). The sum of supplementary angles is $180^{\circ}$. So $m\angle CDG=180^{\circ}-m\angle DGF$.

Step3: Calculate the measure of $\angle CDG$

Substitute $m\angle DGF = 132^{\circ}$ into the formula: $m\angle CDG=180 - 132=48^{\circ}$.

Answer:

$48$