The AOB angle is 60 degrees. The OC beam is the bisector of the AOK angle, and the OC

The AOB angle is 60 degrees. The OC beam is the bisector of the AOK angle, and the OC beam is the bisector of the BOC angle. Find the value of the angle KOС.

Angle AOB = AOK + KOB.

Since the OC ray is the bisector of the angle AOK = α, therefore, AOK = AOC + KOC = α / 2 + α / 2.

That is, KOC = α / 2.

Since the ray ОK is the bisector of the angle BOC = β, therefore, BOC = KOB + KOC = β / 2 + β / 2.

That is, KOC = β / 2.

Hence, α / 2 = β / 2, α = β.

Then,

AOB = AOK + KOB = AOC + KOC + KOB = 2 * KOС + α / 2 = 2 * KOС + α = 2 * α / 2 + α / 2 = 3 * α / 2

3 * α / 2 = 60º.

α = 40º.

Then, the angle KOC = α / 2 = 20º.