# Angle at the apex of an isosceles triangle = 94 degrees, find the acute angle formed by the bisectors

August 23, 2021 | education

| **Angle at the apex of an isosceles triangle = 94 degrees, find the acute angle formed by the bisectors of the angles at the base of the triangle.**

Since the triangle ABC is isosceles, its angles at the base are equal, then the angle BAC = BCA = (180 – ABC) / 2 = (180 – 94) / 2 = 43.

AM and SC are the bisectors of the angles at the base, then the angle ОАС = OCA = 43/2 = 21.5.

In the AOC triangle, the AOC angle = (180 – OAC – OCA) = (180 – 21.5 – 21.5) = 137.

The angles AOC and MOC are adjacent, the sum of which is 180, then the angle MOC = (180 – 137) = 43.

Answer: The acute angle between the diagonals is 43.

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