We know that AB || CD and GE is the transversal
From the figure we know that ∠EGF and ∠GED are interior angles
So we get
∠EGF + ∠GED = 180o
By substituting the values
∠EGF + 130o = 180o
On further calculation
∠EGF = 180o – 130o
By subtraction
∠EGF = 50o
Therefore, ∠EGF = 50o