The value of x is 1. Substituting x into the expression for IJ, we find IJ = 15. Therefore, the measure of IJ is 15.
Since I and J are the midpoints of FH and GH respectively, then FG = 2IJ.
Substituting the expressions that were given for FG and IJ, we get:
35 - 5x = 2(21 - 6x)
35 - 5x = 42 -12x
7x = 7
x = 1
Plugging the value of x back into the expression that was given for IJ, we get:
IJ = 21 - 6(1)
IJ = 21 - 6
IJ = 15
Therefore, the measure of IJ is 15.