Question

: A DEF. Stde EFis Side EF is extended to G P.T LOFG LEEF+ LEDF​

Answer 1

Statement:- In a Triangle, The Sum of two opposite interior angles is equal to exterior angle.

Given:- DEF is a Triangle & Side EF is extended to G.

Required To Prove:- ∠DFG = ∠DEF+∠FDE

Proof:-

WKT

Sum of all interior angles in a triangle is 180°

∠DEF+∠FDE+∠DFE = 180° ➝[1]

Sum of Linear Paired Angles is 180°

∠DFE+∠DFG = 180° ➝[2]

From ① & ②

∠DEF+∠FDE+∠DFE = ∠DFE+∠DFG → 180°

∠DEF+∠FDE = ∠DFE+∠DFG-∠DFE

∠DEF+∠FDE = ∠DFG

• $\longmapsto\;\bold{∠DEF+∠FDE = ∠DFG}$

Hence, Proved.

$\tt{@MrMonarque}$

Hope It Helps You ✌️

Answer 2

We Know That :- 

In a Triangle, The Sum of two opposite interior angles is equal to exterior angle.

Given :- 

DEF is a Triangle & Side EF is extended to G.

To Prove :- 

∠DFG = ∠DEF+∠FDE

Proof:-

We know that

Sum of all interior angles in a triangle is 180°

$\sf ∠DEF+∠FDE+∠DFE = 180° \: - eq \: [1]$

Sum of Linear Paired Angles is 180°

$\sf ∠DFE+∠DFG = 180° - eq \: [2]$

From ① & ②

$\sf ∠DEF+∠FDE+∠DFE = ∠DFE+∠DFG → 180°$

$\sf ∠DEF+∠FDE = ∠DFE+∠DFG-∠DFE$

$\sf ∠DEF+∠FDE = ∠DFG$

∴$\sf \fbox{∠DEF+∠FDE = ∠DFG}$

Hence Proved.

$\fbox \orange{ \sf @IIMrVelvetII}$

$\fbox \green{ \sf Thank You!!!}$