The angle obtained at the intersection of two bisectors of a triangle is 128 °. Find the third corner of the triangle.

univerkov | April 9, 2021 | education

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

AOC + OAC + OCA = 180.

ОАC + ОCА = 180 – 128 = 52.

Since AK and CM are the bisectors of the angles, the angle BAC = ОАC, and the angle ВCМ = ОCА.

Then ВAK + ВСМ = ОАC + ОСА = 52.

Then the sum of the angles BAC + BCA = OAC + OCA + BAC + BCM = 52 + 52 = 104.

Angle ABC = 180 – (BAC + BCA) = 180 – 104 = 76

Answer: The third angle is 76.

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