Question

hey guys plz help me in this question with full explanation

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truth​

Answer 1

Given:- BE and CF are bisectors of angle ABC and angle ACD

TO PROVE:-<BEC=1/2<BAC

PROOF:- <ACD=<ABC+<BAC[Sun of two opposite interior angles of a triangle is equal to its exterior angle]

=> 1/2<ACD=1/2(<ABC+<BAC)

=> <ECD=1/2(<ABC+<BAC) ............ (1)

SINCE, <ECD is the exterior angle of triangle EBC

=> <ECD= <ECB+<EBC[Sum of two opposite side of a triangle is equal to its exterior angle]

=> <ECD=1/2(<ABC+<BEC) ............. (2)

From (1) &(2) we get,

1/2<ABC+1/2<BAC=1/2<ABC+1/2 <BEC

= <BEC=1/2 <BAC