The bisector of angle B of triangle ABC intersects the circle circumscribed about this triangle at point K.

The bisector of angle B of triangle ABC intersects the circle circumscribed about this triangle at point K. Find the angles of triangle AKS if angle ABC is 80 degrees.

By the condition of the problem ВK is the bisector of the angle ABC, we obtain: ∠ ABK = ∠ CBK = 40 °.
The angle ABK is inscribed in a circle and rests on the arc AK, the angle ACK rests on the same arc, which means that its degree measure is also 40 °. Similarly, we consider the angle of the СВK. It rests on the arc СK, on which the angle СAK = 40 ° rests. Two angles of the triangle AKС are found, the third angle AKС is 180 ° – 80 = 100 °.
Answer: the angles of the AKС triangle are 40 °, 40 °, 100 °.