It is known that in a triangle ABC: AB = BC, angle C is 70 degrees, AD is the bisector of angle A. Find the angle ADB.

Given: triangle ABC;
AB = BC,
angle С = 70 degrees,
AD is the bisector of angle A.
Find the angle ADB
Solution: Since AB = BC, triangle ABC is isosceles. In an isosceles triangle, the angles at the base are equal. Then the angle C = angle A = 70 degrees. According to the condition of the problem, AD is the bisector of angle A, therefore the angle BAD = DAC = 70 degrees: 2 = 35 degrees because the bisector divides the angle in half.
Answer: 35 degrees.