In the given figure AB//CD; EF ⊥ CD and ∠GED = 126°, find ∠AGE,

1.	In the given figure AB//CD; EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
Answer» Given that EF ⊥ CD; ∠GED = 126° i. e., ∠FED = 90° and ∠GEF = ∠GED – ∠FED ∠GEF = 126° – 90° = 36° In ∆GFE ∠GEF + ∠FGE + ∠EFG = 180° 36 + ∠FGE + 90° = 180 ∠FGE = 180° – 126° = 54° ∠AGE = ∠GFE + ∠GEF (exterior angle in ∆GFE) = 90°+ 36°= 126°

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

Answer»

Given that EF ⊥ CD; ∠GED = 126°

i. e., ∠FED = 90°

and ∠GEF = ∠GED – ∠FED ∠GEF = 126° – 90° = 36°

In ∆GFE ∠GEF + ∠FGE + ∠EFG = 180°

36 + ∠FGE + 90° = 180

∠FGE = 180° – 126° = 54°

∠AGE = ∠GFE + ∠GEF

(exterior angle in ∆GFE)

= 90°+ 36°= 126°