In an isosceles triangle ABC with base AC, the median BD is half of the side AC. Find the angles of triangle ABC.

Let the length of the base AC = X cm.

Since BD is the median of the ABC triangle, then AD = CD = X / 2 cm.

By condition, the length of the median BD = AC / 2 = X / 2 cm.

Since the ABC triangle is isosceles, then its median BD is also its height, and then the BCD triangle is rectangular, whose legs are equal, SD = BD = X / 2.

Hence the acute angles of the triangle are 45.

Angle ВСD = CBD = 45

The median ВD is also the bisector of the ABC angle, then the ABC angle = 2 * CBD = 2 * 45 = 90.

Answer: Angle ABC is 90.