The bisectors of angles A and C of triangle ABC intersect at point O. Find the angle AOC equal to 110 degrees.

univerkov | September 27, 2021 | education

The sum of the interior angles of a triangle is 180.

Then the sum of the angles (BAC + BCA) = (180 – ABC) = (180 – 110) = 70.

Since AM and CK are the bisectors of the angles BAC and BCA, then the angle OAC = BAC / 2, the angle OCA = BCA / 2.

Then the sum of the angles (OAC + OCA) = (BAC / 2 + BCA / 2) = (BAC + BCA) / 2 = 70/2 = 35.

Then the angle AOC = 180 – 35 = 145.

Answer: The AOC angle is 145.

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