Line GE is the perpendicular bisector of triangle LGK. This means that Line GE divides angle LGK into two equal halves. Thus, triangle LGE is congruent to triangle KGE. Therefore,
GL = GK
From the information given,
GL = 4x - 2
GK = 2x + 8
Thus,
4x - 2 = 2x + 8
4x - 2x = 8 + 2
2x = 10
x = 10/2
x = 5
If GE = 3x + 2, if we substitute x = 5, then
GE = 3 * 5 + 2 = 15 + 2
GE = 17
Substituting x = 5 into GL = 4x - 2,
GL = 4 * 5 - 2 = 20 - 2
GL = 18
Since GC is the perpendicular bisector of triangle JGL, it means that triangle JGC is congruent to triangle LGC
Thus, JG = LG
GJ = GL
GJ = 18