Answer 1

In △ABC, AB = AC
∴ ∠ABC = ∠ACB            (Angles opposite to equal sides are equal) 
⇒ x = 50^∘
In △BDC, DB = DC
∴ ∠DBC= ∠DCB            (Angles opposite to equal sides are equal) 
⇒ y = 60^∘
Now, ∠ABD = ∠ABC + ∠DBC
= 50^∘ + 60^∘
= 110^∘
Also, ∠ACD = ∠ACB + ∠DCB
= 50^∘ + 60^∘
= 110^∘
Hence, the values of x and y are 50^∘ and 60^∘ respectively.