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

| September 29, 2021 | education

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.



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