Question

In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.

Answer 1

∠GED = 126°

AB || CD is given.

∴ ∠AGE = ∠GED        ...(Alternate angles)

Hence:, ∠AGE = 126°

∠GED = 126°

∠GED = ∠GEF + ∠FED = 126°

∠GEF + ∠FED = 126°

∠GEF + 90° = 126°        ...(∵ EF ⊥ CD ∴ ∠FED = 90°)

∠GEF = 126° − 90°

∠GEF = 36°

Now,

∠AGE + ∠FGE = 180°      ...(Linear pair)

126° + ∠FGE = 180°

∠FGE = 180° − 126°

∠FGE = 54°

∴ ∠AGE = 126°, ∠GEF = 36° and ∠FGE = 54°.