In triangle ABC, D belongs to [AC]; E belongs to [BC]; such that | DE | = | EC |. What is the angle ABC

In triangle ABC, D belongs to [AC]; E belongs to [BC]; such that | DE | = | EC |. What is the angle ABC, if the angle BAC = 50 degrees; angle ADE = 140 degrees?

The angle ADH and CDE are adjacent angles, the sum of which is 180, then the angle CDE = 180 – 140 = 40.

Since, by condition, DE = CE, then the triangle CDE is isosceles, which means the angle DCE = CDE = 40.

Then the angle ABC = 180 – BAC – ACB = 180 – 50 – 40 = 90.

Answer: the angle ABC is 90.