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ABC is equilateral => angle A = angle B = angle C = 60
ACD is also equilateral => angle A = angle B = angle C = 60
=> angle A in ABD = 120
AB = AD => ABD is isosceles => angle B = angle D = 180 - 120 / 2 = 30
AB = BC = AC => ABC is an equilateral triangle=> angle BAC is 60 degree
that means angle DAC = 60 degree
As per the rule - angle made by the arc on center is twice the angle made by the same arc on the circumference. Here the angle DAC made by the arc DC on the center is 60 degree. So the DBC = 30.
As angle ABC = 60 degree, the angle ABD = x = 30 degree
from given info and figure it is clear that AB=BC=AC=AD=DC. Here basically BD connects two opposite vertices of 2 equi. triangles with common base AC. Hence, it should be dividing the the angles B and D into half. i.e. 60/2 = 30