In triangle ABC, angle C is equal to 45, bisector BD is equal to side AB. What are angles A and B equal to?

Let the value of the angle ABC = 2 * X0.

The segment BD is the bisector of the angle ABC, then the angle ABD = CBD = 2 * X / 2 = X0.

Since, by condition, AB = BD, the triangle ABD is isosceles, and therefore the angle BAD = BDA = (180 – X) / 2 = (90 – X / 2) 0.

The sum of the interior angles of the triangle ABC is 180, then:

45 + (90 – X / 2) + 2 * X = 180.

1.5 * X = 45.

X = 45 / 1.5 = 30.

Angle ABC = 2 * 60 = 60, angle BAC = (90 – 30/2) = 90 – 15 = 75.

Answer: Angle A is 75, Angle B is 60.