Ray OK is the bisector of the angle, the sides of which are the bisectors of the adjacent angles

Ray OK is the bisector of the angle, the sides of which are the bisectors of the adjacent angles AOC and COB. Calculate the degree measure of the AOC angle if the AOC angle is 75

1. Based on the condition of the problem, we get that the sum of the angles, namely the AOK angle, the AOC angle, the OWL angle and the AOK angle, will be equal to 360 degrees. And the angles are adjacent, and we know that the sum of adjacent angles is 180 degrees.
2. If the angle AOK is 75 degrees, then its adjacent angle AOK will be:
180 – 75 = 105 degrees;
3. The BOC angle is adjacent to the KOB angle, which means that we can find it:
180 – 105 = 75 degrees;
4. So it remains for us to find the angle of the AOC:
180 – 75 = 105 degrees since it is adjacent to the COB angle.
Answer: AOC angle = 105 degrees.