In isosceles triangle ABC with base AC, bisector BL is drawn, and in triangle BLC, bisector LD. Find the angle BLD.

It is known that ABC is an isosceles triangle, AC is the base of this isosceles triangle, and BL is a bisector drawn from apex B of triangle ABC to the base of AC.

By the property of the bisector drawn from the apex of an isosceles triangle, BL is also the median (then L is the middle of the AC) and height (therefore, the angle BLA = angle BLC = 90 °).

In triangle BLC, the bisector LD is also drawn to the BC side. By definition, the bisector divides the angle into two equal angles, which means that the angle BLD = 90: 2 = 45 °.

Answer: 45 °.