# Bisectors AA1 and BB1 of triangle ABC meet at point O. Find the angles AOB, AOC, and BOC, assuming angle

Bisectors AA1 and BB1 of triangle ABC meet at point O. Find the angles AOB, AOC, and BOC, assuming angle A = 50 degrees and angle B = 60 degrees.

To solve the problem, consider the figure.

Since AA1 and BB1 are the bisectors of the corresponding angles, they divide the angles ABC and BAC in half.

Then the angle ABO = ABC / 2 = 60/2 = 30.

Angle BAO = BAC / 2 = 50/2 = 25.

Then the value of the angle AOB = 180 – ABO – BAO = 180 – 30 – 25 = 125.

Let’s draw a straight line from point C to point O, which will be the bisector of the angle BCO, since the bisectors of the triangle intersect at one point.

Angle BCO = 180 – ABC – BAC = 180 – 60 – 50 = 70.

Then the angle ВСО = АСО = 70/2 = 35.

Angle AOC = 180 – OAC – OCA = 180 – 25 – 35 = 120.

Angle BOC = 180 – OBC – BCO = 180 – 30 – 35 = 115

Check: 115 + 120 + 125 = 360.

Answer: Angle AOB = 125, AOC = 120, BOC = 115. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.