Let BD intersects AC at X.
Triangles, BCX and ABX are congruent,
angle AXB = angle BXC = 90 degree (as BC = CD)
and BX is common side for both triangles.
this implies, angle ABX = CBX ..... (i)
Triangle ABC is equilateral triangle (as AB=BC=AC)
This implies angle ABC = 60 degree .... (ii)
From (i) and (ii), we can say that angle ABX = CBX = 30
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