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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