In a triangle ABC, AB = BC, BD and AE are the bisectors of the triangle, AD = BE. Find corner C.

Since in the triangle ABC, AB = BC, therefore, this triangle is isosceles with the base AC. According to the theorem (properties of bisectors in an isosceles triangle), the bisector, which is drawn to the base, is also the median and height.

Also, according to the condition of the problem, AD = BE, therefore, triangle ABC is equilateral, and in an equilateral triangle all angles are equal, then

180 ° (sum of angles in a triangle) / 3 = 60 °.

Answer: angle C is 60 °.