Question

In the figure, if AB || CD, EF ⊥ CD and ∠GED = 126°. Find ∠ AGE, ∠GEF and ∠FGE.

Answer 1

In the given figure, AB || CD, EF ⊥ CD 

and ∠GED = 126° 

∠AGE = ∠LGE (Alternate angle) 

∴ ∠AGE = 126° 

Now, ∠GEF = ∠GED – ∠DEF 

= 126° – 90° = 36° (∵ ∠DEF = 90°) 

Also, ∠AGE + ∠FGE = 180° (Linear pair axiom) 

⇒126° + FGE = 180° 

⇒ ∠FGE = 180° – 126° = 54°