In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If BD=BC, what is the measure, in degrees, of angle A?
(Be careful with this one.) 
+1641 The answer from the above link is incorrect!!!
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In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If BD=BC, what is the measure, in degrees, of angle A?
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AB = AC BD = BC AD = BD = BC
The sum of the interior angles of each triangle is 5x
5x = 180 x = 36 ∠A = 36º
