The given figure shows two isosceles triangles. Triangle abc in which ab = ac and in triangle dbc db - dc. What is the measure of angle bac.

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in this figure DB=DC 
then angle DBA= angle DCA = 32 degree
let angle ABC= x
we know that ab=ac 
then ACB = x because ab=ac
42+32+x+32+x=180
x = 35
x+x+angle BAC = 180
35+35+angle BAC = 180 
BAC = 110
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