In triangle ABC, angle A is 76 degrees, angle B is 65 degrees, AD BE CF bisectors intersecting

In triangle ABC, angle A is 76 degrees, angle B is 65 degrees, AD BE CF bisectors intersecting at point O. Find angle AOF.

Angle C of triangle ABC is equal to:

С = 180º – (76º + 65º) = 180º – 141º = 39º.

Angle ОАС = 76º / 2 = 38º.

Angle OCA = 39º / 2 = 19.5º.

Then, in the AOC triangle, the AOC angle is:

AOC = 180º – (ОАС + OCA) = 180º – (38º + 19.5º) = 180º – 57.5º = 122.5º.

AOF is an angle adjacent to AOC, so AOF = 180º – 122.5º = 57.5º.