BD is the bisector of an isosceles triangle ABC (AB = BC). AC = 18cm. The DBC angle is 21 degrees.

BD is the bisector of an isosceles triangle ABC (AB = BC). AC = 18cm. The DBC angle is 21 degrees. Find the angle ABD, angle ADB, side AD.

Since, by condition, triangle ABC is isosceles, the bisector BD, angle ABC is also its median and height.

Then the angle ABD = DBC = 21, the angle ADB = 90, since BD is the height of the triangle, which means it is perpendicular to AC, and the segment AD = CD = AC / 2 = 18/2 = 9 cm, since BD is the median, which means divides the speaker in half.

Answer: Angle ABD = 21, angle ADB = 90, AD = 9 cm.