Since, AB=AC, ∴∠ABC=∠ACB=2x (let) Since, BE is an angle bisector. ∴∠EBC=
2x
2
=x∘ Since, CE is an angle bisector. ∴∠ACE=∠ECD=y (let) Given, ∠BEC=35∘ ∴ In △BEC, x+2x+y+35=180∘ [∵ angle sum of triangle ] 3x+y=180∘−35∘=145∘ Since, BD is a straight line. 2x+2y=180∘ x+y=90∘ ∴y=90∘−x Put this value in Eq. (i) 3x+90−x=145∘ ∴2x=145∘−90∘=55∘ ∴∠ABC=55∘