In Fig. 6.30, if AB || CD, EF ⊥ CD and∠ GED = 126°, find ∠ AGE, ∠ GEF and ∠ FGE.

It is given in the question that:

AB || CD

EF perpendicular CD

∠GED = 126^o

Now, according to the question,

∠FED = 90^o (EF perpendicular CD)

Now,

∠AGE = ∠GED (Since, AB parallel CD and GE is transversal, hence alternate interior angles)

Therefore,

∠AGE = 126^o

And,

∠GEF = ∠GED - ∠FED

∠GEF = 126^o – 90^o

∠GEF = 36^o

Now,

∠FGE + ∠AGE = 180^o (Linear pair)

∠FGE – 180^o – 126^o

∠FGE = 54^o