Answer: 26
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Explanation:
Angles EDF and FDG are congruent due to the similar angle markers. Because of these congruent adjacent angles, we can use the angle bisector theorem to solve for x.
DE/FE = DG/FG
24/x = 54/(x+10)
24(x+10) = 54x .... cross multiplication
24x+240 = 54x
240 = 54x-24x
240 = 30x
30x = 240
x = 240/30
x = 8
From there we can say:
- EF = x = 8
- FG = x+10 = 8+10 = 18
- EG = EF+FG = 8+18 = 26
