Given :
AB || CD, ∠GED = 126°.
Since,
EF ⊥ CD.
∴ ∠FED = 90°.
From figure,
⇒ ∠GED = ∠GEF + ∠FED
⇒ ∠GEF = ∠GED - ∠FED
⇒ ∠GEF = 126° - 90°
⇒ ∠GEF = 36°.
AB and CD are parallel lines cut by a transversal GE, thus the pair of alternate interior angles formed are equal.
⇒ ∠AGE = ∠GED
⇒ ∠AGE = 126°.
From figure,
⇒ ∠AGE + ∠FGE = 180° [Linear pairs]
⇒ 126° + ∠FGE = 180°
⇒ ∠FGE = 180° - 126° = 54°.
Hence, ∠AGE = 126°, ∠GEF = 36° and ∠FGE = 54°.