Question

the side BC of ABC is produced such that D is on rayBC the bisector of angle A meets BC at D prove that angle abc + angle BAC equal to 2 angle A L C

Answer 1

To Prove ABC + ACD = 2A C  

AL in the angle bisector of A, so let BAL = LAC = x

Then, using exterior angle property

∠ALC = x  +  [alpha]               ..(1)

Similarly

 ∠ACD= 2x +                             ..(2)

Hence from (1) and (2), we get

ABC + ACD = 2ALC

(i.e.)

 ( [alpha] ) + (2x +  [alpha] ) = 2(x + [alpha] )

HENCE PROVED