Question 1205645
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I'll assume the order of the points (either clockwise or counterclockwise) is D, E, F, G.


Perhaps your diagram looks something like this
{{{
drawing(400,400,-5,5,-5,5,
circle(-4,-2,0.05),circle(-4,-2,0.07),circle(-4,-2,0.09),circle(-4,-2,0.11),circle(-4,-2,0.13),circle(-4,-2,0.15),circle(-3,2,0.05),circle(-3,2,0.07),circle(-3,2,0.09),circle(-3,2,0.11),circle(-3,2,0.13),circle(-3,2,0.15),circle(4,2,0.05),circle(4,2,0.07),circle(4,2,0.09),circle(4,2,0.11),circle(4,2,0.13),circle(4,2,0.15),circle(3,-2,0.05),circle(3,-2,0.07),circle(3,-2,0.09),circle(3,-2,0.11),circle(3,-2,0.13),circle(3,-2,0.15),

line(-4,-2,-3,2),line(-3,2,4,2),line(4,2,3,-2),line(3,-2,-4,-2),

line(-4.04,-0.18,-3.46,0.24),line(-3.46,0.24,-3.14,-0.26),line(2.94,-0.14,3.54,0.22),line(3.54,0.22,3.86,-0.28),line(-1.34,-1.5,-0.98,-1.96),line(-0.98,-1.96,-1.44,-2.44),line(-0.56,-1.5,-0.32,-1.96),line(-0.32,-1.96,-0.64,-2.46),line(-0.02,2.46,0.18,2),line(0.18,2,-0.14,1.56),line(0.98,2.44,1.18,2),line(1.18,2,0.86,1.56),

locate(-4.38,-2.16,"D"),locate(-3.26,2.38+0.2,"E"),locate(3.96,2.36+0.2,"F"),locate(3.1,-2.1,"G")

)

}}}

If so, then DE is parallel and opposite FG. 
With any parallelogram, the opposite sides are congruent.
DE = FG
3x+2 = 2x+8
3x-2x = 8-2
x = 6


Also, opposite parallel sides EF and DG are congruent.
EF = DG
5x-6 = 4x 
5x-4x = 6
x = 6


When x = 6, we have the following side lengths
DE = 3x+2 = 3*6+2 = 20
FG = 2x+8 = 2*6+8 = 20
This confirms the 1st equation.
EF = 5x-6 = 5*6-6 = 24
DG = 4x = 4*6 = 24
This confirms the 2nd equation.



Summary:
x = 6
DE = 20
EF = 24
FG = 20
DG = 24
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