In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If AD=DC, what is the measure, in degrees, of angle A?
For BD to bisect angle(B) and also to bisect the side AC, triangle(ABC) must be an isosceles triangle with
AB = BC.
Since AB = AC, all three sides, AB, BC, and AC are equal in length.
This means that triangle(ABC) is an equilateral triangle, so each of its angles must equal 60o.