Question

if $overleftrightarrow{bd}$ and $overleftrightarrow{eg}$ are parallel lines and $mangle gfc = 56^{circ}$, what is $mangle bcf$?

Explanation:

Step1: Identify angle - relationship

$\angle GFC$ and $\angle BCF$ are same - side interior angles.

Step2: Recall property of same - side interior angles

For parallel lines $\overleftrightarrow{BD}$ and $\overleftrightarrow{EG}$, same - side interior angles are supplementary, so $m\angle GFC+m\angle BCF = 180^{\circ}$.

Step3: Solve for $m\angle BCF$

$m\angle BCF=180^{\circ}-m\angle GFC$. Substitute $m\angle GFC = 56^{\circ}$ into the equation. Then $m\angle BCF=180 - 56=124^{\circ}$.

Answer:

$124^{\circ}$