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2012 Paper 2 Q22

Solution: <ABE = (180-112)/2 = 34, <FCB = 180-90-34 = 56, so <DCF = 90-56 = 34

Let DA be 1 unit, so DC = DA = AB = 1,

DF/DC = tan34, FA/AB = tan <ABF

so DF = tan 34, FA = tan <ABF

Since DF + FA = 1, then tan 34 + tan <ABF =1

Solving this gives <ABF = 18.03 = 18 (Ans: B)