1) < BEF = < GFE and < AEG = < FGE [ a transversal cutting two parallel lines makes alternate interior angles equal]
Since EF = FG then < FGE = < GEF [ when two sides of a triangle are equal, the angles opposite those sides are also equal]
But < AEG = < FGE....so ..... <GEF = < AEG as well
And we have that
< GFE + < FGE + < GEF = 180 and by substitution
[100 + x ] + x + x = 180
100 + 3x = 180 subtract 100 from each side
3x = 80
x = 80/3 = about 26.66°