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 \\) submit answer

Explanation:

Step1: Find $\angle BCF$ via triangle sum

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

Step2: Use parallel lines property

Since $\overline{AD} \parallel \overline{EG}$, consecutive interior angles are supplementary.
$$\angle GFC + \angle BCF = 180^\circ$$
$$\angle GFC = 180^\circ - 72^\circ = 108^\circ$$

Answer:

$108$