Answer:
DE = 9
Explanation:
Given quadrilateral DEFG with DG≅EF, ∠FDG≅∠DFE, and markings EF=(6x+4), DG=(4x+8), and FG=(4x+1), you want the measure of DE.
Parallelogram
The given congruences mean that the figure DEFG is a parallelogram. Opposite sides are the same length.
EF = DG
6x +4 = 4x +8
2x = 4 . . . . . . . . subtract (4x+4)
x = 2 . . . . . . . . divide by 2
Now, we can find FG.
FG = 4x+1 = 4(2) +1 = 9
Opposite side DE is the same length:
DE = 9
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Additional comment
You can prove ΔEFD ≅ ΔGDF using SAS. Then CPCTC tells you corresponding parts of the triangles are congruent: DE≅FG.