Question

finding angles (level 1)
question
in the diagram below, (overline{ad} parallel overline{eg}), (\text{m}angle bfc = 71^circ) and (\text{m}angle fbc = 37^circ). find (\text{m}angle gfc).
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
answer
attempt 1 out of 2
(\text{m}angle gfc = square^circ)

Explanation:

Step1: Find ∠BCF via triangle sum

The sum of angles in a triangle is $180^\circ$. For $\triangle BFC$:
$$\angle BCF = 180^\circ - \angle BFC - \angle FBC$$
$$\angle BCF = 180^\circ - 71^\circ - 37^\circ = 72^\circ$$

Step2: Use alternate interior angles

Since $\overline{AD} \parallel \overline{EG}$, $\angle BCF$ and $\angle GFC$ are alternate interior angles, so they are equal:
$$\angle GFC = \angle BCF$$

Answer:

$72$