Question

The side of a triangle ABC is produced to d the bisectors of angle A meets d at l prove that angle ABC plus angle ACD is equal to two times of angle alc

Answer 1

To Prove ∠ABC + ∠ACD = 2∠ALC

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

Then, using exterior angle property  

∠ALC = x  + α  ---------- (1)              

Similarly  

 ∠ACD= 2x +  α  -----------(2)        

Hence from (1) and (2), we get  

∠ABC + ∠ACD = α + 2x + α = 2(x+α)

∠ABC + ∠ACD = 2 ∠ALC

HENCE PROVED