Answer: C. 47 degrees
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Explanation:
We need to find the values of x and y first
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Let's find x.
Segment IG is the same length as segment GH, as shown by the tickmarks
IG = GH
3x = 5x-10
3x-5x = -10
-2x = -10
x = -10/(-2)
x = 5
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Now onto finding y.
Ray BD is the bisector of angle ABC. The angle ABC is cut into two equal halves which are angle ABD and angle DBC
angle ABD = angle DBC
10y = 8y+4
10y-8y = 4
2y = 4
y = 4/2
y = 2
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We have enough info to find angle FBA
angle FBA = 7x+6y
angle FBA = 7*5+6*2
angle FBA = 35+12
angle FBA = 47 degrees
