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

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°.