Answer:
EF = 8
Step-by-step explanation:
FD is an angle bisector and divides the opposite side of the angle into segments that are proportional to the other 2 sides, that is
[tex]\frac{DE}{DG}[/tex] = [tex]\frac{EF}{FG}[/tex] , substitute values
[tex]\frac{24}{54}[/tex] = [tex]\frac{x}{x+10}[/tex] ( cross- multiply )
54x = 24(x + 10) ← distribute
54x = 24x + 240 ( subtract 24x from both sides )
30x = 240 ( divide both sides by 30 )
x = 8
Thus EF = x = 8
