You are given an obtuse isosceles triangle ABC. On the base of the CB, a CD segment equal to the lateral side is laid.

You are given an obtuse isosceles triangle ABC. On the base of the CB, a CD segment equal to the lateral side is laid. The median CE is drawn in triangle ACD. Find the angle ABC if the angle ACE is 16 degrees.

Let’s connect points A and D. Triangle ACD is isosceles, since, by condition, AC = CD.

Then the median CE of the isosceles triangle ACD is also the bisector of its angle ACD.

Hence the angle DCE = ACE = 16, and therefore the angle ACD = 2 * 16 = 32.

Triangle ABC, by condition is isosceles, then its angles at the base are equal.

Angle ABC = ACD = ACB = 32.

Answer: The angle ABC is 32.