In the figure, AB = BC, BD is the bisector of angle ABC, DC = 35, BC = 80. Find AD.

Angle AD = angle DC = 35 degrees, because the bisector AD is drawn from the apex of the angle ABC to the base of the AC, and since the bisector drawn from the apex of the angle to the base of the angle is the median and height, therefore, the triangle ABC is isosceles. In an isosceles triangle, the angles at the base are equal.



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