Bisectors AD and BE of triangle ABC intersect at point O. Find the angle C of the triangle if AOE = 50

We denote the angle OAE = x = the angle OAB,

angle EOD = angle AOB = 180 – 50 = 130,

then angle ABO = angle OBD = 180 – 130 – x = 50 – x,

angle AOE = angle BOD = 50,

It follows from this that the angle BОO = 180 – 50 – (50 – x) = 80 + x,

Hence the angle ADC = 180 – (80 + x) = 100 – x,

Then the angle C = 180 – x – (100 – x) = 80.

Answer: Angle C of triangle ABC is 80 degrees.