Consider the figure

Given

AB = AC,DB = DC and given to find the ratio

∠ABD = ∠ACD

Now, ΔABC and ΔDBC are isosceles triangles since AB = AC and DB = DC respectively

⇒ ∠ABC =∠ACB and ∠DBC = ∠DCB [angles opposite to equal sides are equal]

Now consider,

∠ABD : ∠ACD