Question

look at this diagram: if $overleftrightarrow{bd}$ and $overleftrightarrow{eg}$ are parallel lines and $mangle bcf = 126^{circ}$, what is $mangle gfc$?

Explanation:

Step1: Identify angle - relationship

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

Step2: Apply property of parallel lines

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

Step3: Solve for $m\angle GFC$

$m\angle GFC = 180^{\circ}-m\angle BCF$. Substitute $m\angle BCF = 126^{\circ}$ into the equation: $m\angle GFC=180 - 126=54^{\circ}$.

Answer:

$54$