Question

please help me solve this

Answer 1

Hi.

∠FEB + ∠DFE = 180°            --(eq.1)
------because: sum of angles on same side of transversal is 180°....

∠FEB = ∠FEG + ∠GEB            --(eq.2) 
and,
∠EFD = ∠EFG + ∠GFD            --(eq.3)

Put (eq.2) and (eq.3) in (eq.1).........

∠FEG + ∠GEB + ∠EFG + ∠GFD  = 180°              --(eq.4) 

Now, 
∠FEG = ∠GEB            --(eq.5) 
------------because: EG is the bisector of ∠FEB

and,

∠EFG = ∠GFD            --(eq.6) 
------------because: FG is the bisector of ∠FED

Now, Put (eq.5) and (eq.6) in (eq.4).........

∠FEG + ∠FEG + ∠EFG + ∠EFG  = 180° 
2(∠FEG + ∠EFG) = 180°
∠FEG + ∠EFG = 180 ÷ 2
∠FEG + ∠EFG = 90° --------(eq.7)

Now, in ΔEFG,
∠FEG + ∠EFG  + ∠EGF = 180°
------because of angle sum property of triangles.....
but, ∠FEG + ∠EFG = 90° as in (eq.7)....

This way,

90° + ∠G = 180°
∠G = 180° - 90° = 90°
∠G = 90°

Hence Proved......

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