Question

look at this diagram: if $overleftrightarrow{bd}$ and $overleftrightarrow{eg}$ are parallel lines and $mangle efc = 64.6^{circ}$, what is $mangle gfc$?

Explanation:

Step1: Recall angle - addition property

$\angle EFC$ and $\angle GFC$ are a linear - pair of angles. A linear pair of angles are supplementary, which means their sum is $180^{\circ}$. So, $m\angle EFC + m\angle GFC=180^{\circ}$.

Step2: Solve for $m\angle GFC$

We know that $m\angle EFC = 64.6^{\circ}$. Then $m\angle GFC=180^{\circ}-m\angle EFC$. Substitute $m\angle EFC = 64.6^{\circ}$ into the equation: $m\angle GFC = 180 - 64.6=115.4^{\circ}$.

Answer:

$115.4$