The angle at the apex of an isosceles triangle is 94 degrees, find the acute angle

The angle at the apex of an isosceles triangle is 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 of the AC are equal.

Angle BAC = BCA = (180 – 94) / 2 = 43.

Since AE and CE, by condition, are the bisectors of the angles at the base, then the angle OAC = BAC / 2 = 43/2 = 21.5.

Angle OCA = BCA / 2 = 43/2 = 21.5.

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

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

Answer: The acute angle at the intersection of the bisectors is 43.