In Fig. 9.41, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find a and y.
Given,
AB || DE and,
BD || FG
∠FGH + ∠FGE = 180o (Linear pair)
125o + y = 180o
y = 55o
∠ABC = ∠BDE (Alternate angles)
∠BDF = ∠EFG = 55o (Alternate angles)
∠EFG + ∠FEG = 125o (By exterior angle theorem)
55o + ∠FEG = 125o
∠FEG = x = 70o
Thus, x = 70o and y = 55o.