Question

in the diagram below, $ad \parallel eg$, $m\angle bfc = 75^\circ$ and $m\angle gfc = 38^\circ$. find $m\angle fbc$.\
step angle reason\
1 $m\angle bfc = 75^\circ$ given\
2 $m\angle gfc = 38^\circ$ given\
try $m\angle\square=\square^\circ$ select a reason\
e f g\
a b c d\
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Explanation:

Step1: Calculate ∠BFG

$m\angle BFG = m\angle BFC + m\angle GFC = 75^\circ + 38^\circ = 113^\circ$

Step2: Use parallel line property

Since $AD \parallel EG$, consecutive interior angles are supplementary. So $m\angle FBC + m\angle BFG = 180^\circ$

Step3: Solve for ∠FBC

$m\angle FBC = 180^\circ - m\angle BFG = 180^\circ - 113^\circ = 67^\circ$

Answer:

$m\angle FBC = 67^\circ$