3. In Fig. 6.30, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
Solution: Since AB || CD, GE is a transversal. It is given that ∠GED = 126° So, ∠GED = ∠AGE = 126° (As they are alternate interior angles) Also, ∠GED = ∠GEF +∠FED As EF⊥ CD, ∠FED = 90° ∴ ∠GED = ∠GEF+90° Or, ∠GEF = 126° – 90° = 36° Again, ∠FGE +∠GED = 180° (Transversal) Putting the value of ∠GED = 126° we get, ∠FGE = 54° So, ∠AGE = 126° ∠GEF = 36° and ∠FGE = 54°
