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Hint:
angle FGD and angle CGE are vertially opposite. What does that mean?
AB and CD are perpendicular so what is angle CGB ?
Can you work it out now? :)
<EGC = <DGF = 18
<EGC + <BGE = 90
18 + <BGE = 90 subtract 18 from both sides
<BGE = 90 - 18 = 72
