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