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

Since sides AB and BC are equal to each other, triangle ABC is isosceles. This means that angle A is equal to angle C, that is, 70 degrees. In any triangle, the sum of the angles is 180º. Based on this, we find the angle B:

Angle B = 180 – 70 – 70 = 40º.

Consider a triangle ABD. Angle B = 40º. Angle BAD is equal to half the angle A of triangle ABC. Let’s find it:

Angle BAD = 70/2 = 35º.

Knowing the other two corners of the triangle, you can find its third corner. Let’s calculate what the angle ADB is equal to:

Angle ADB = 180 – 40 – 35 = 105º.

Answer: angle ADB = 105º.