# In the figure AB = AC and ∠ACD = 110° find A.

To Find: A
Given: AB = AC and ∠ ACD = 70°
Diagram:

Now, as AB = AC,
∠ABC =  ∠ACB [Angles opposite to opposite sides are equal]........(1)
And,
∠ACB +  ∠ACD = 180º [Sum of angles on a straight line = 180º]
∠ACB + 110º = 180º
∠ACB = 70º
Now, from equation 1,
∠ABC = 70º

we also know that,
∠A + ∠B + ∠C = 180º[Sum of angles of a triangle = 180º]
∠A + 70º + 70º = 180º
∠A = 180º - 140º
∠A = 40º

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