Question

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

Answer 1

∠GED = 126°

∠AGE = ∠GED = 126° [Alternate interior angles]

∠AGE = 126°

∠GED = 126°

∠GEF + ∠FED = 126° [∵∠FED = 90°]

∠GEF + 90° = 126°

∠GEF = 126° – 90° = 36°

∠GEF = 36°

∠GEC + ∠GED = 180° (Linear pair)

∠GEC + 126° = 180°

∠GEC = 180°- 126° = 54°

∠FGE = 54°