In an isosceles triangle ABC, a bisector is drawn from angle A, forming 2 isosceles triangles.

In an isosceles triangle ABC, a bisector is drawn from angle A, forming 2 isosceles triangles. Find the angles of the triangle ABC.

According to the condition AH, the bisector of the angle BAC and forms isosceles triangles ABH and ACH.

Then in the triangle ACH side AH = AC, angle ACH = AHC.

Let the angle ACH = X0, then the angle BAC = ACH = X0, and the angle CAH = (X / 2) 0.

The sum of the inner angles of the triangle is 180, then in an isosceles triangle ACH the sum of the inner angles will be:

(X / 2 + X + X) = 180.

2.5 * X = 180.

X = 180 / 2.5 = 72.

Then in the triangle ABC the angle BAC = BCA = 72, the angle ABC = (180 – 72 – 72) = 36.

Answer: The angles of the triangle ABC are 36, 72, 72.