JAMB - Mathematics (2005 - No. 19)

∠GOK = 85^o (vertical opposite angle ∠s)
∠EOG + ∠GOK + ∠KOF = 180 (∠s on a straight line)
∠EOg + 85^o + 52^o = 180^o
∠EOG + 137^o = 180^o
∠EOG = 43^o