Question

in the diagram below, $\overline{ad}\parallel\overline{eg}$, $m\angle bfc = 73^{circ}$ and $m\angle fbc = 37^{circ}$. find $m\angle gfc$.
step
angle
reason
1
$m\angle bfc = 73^{circ}$
given
2
$m\angle fbc = 37^{circ}$
given
try $m\angle gfc=70^{circ}$ select a reason

Explanation:

Step1: Find the measure of ∠BCF

In △BFC, by the angle - sum property of a triangle (the sum of the interior angles of a triangle is \(180^{\circ}\)).
Let \(m\angle BCF=x\). Then \(m\angle BFC + m\angle FBC+m\angle BCF=180^{\circ}\).
Substitute \(m\angle BFC = 73^{\circ}\) and \(m\angle FBC = 37^{\circ}\) into the equation: \(73^{\circ}+37^{\circ}+x = 180^{\circ}\).
\(x=180^{\circ}-(73^{\circ}+37^{\circ})=180^{\circ}-110^{\circ}=70^{\circ}\). So \(m\angle BCF = 70^{\circ}\).

Step2: Use the property of parallel lines

Since \(\overline{AD}\parallel\overline{EG}\), and \(\overline{CF}\) is a transversal. Then \(m\angle GFC=m\angle BCF\) (alternate - interior angles are equal when two parallel lines are cut by a transversal).

Answer:

\(70\)