The OC beam passes inside the angle AOB, the degree measure of which is 75 degrees.

The OC beam passes inside the angle AOB, the degree measure of which is 75 degrees. Find the angle BOC if the angle AOC = 4 angle BOC.

Let us denote by the variable x the degree value of the AOB angle, which is obtained when the AOB angle is divided by the OC beam.

Therefore, according to the condition of the problem, the degree value of the AOC angle, which was obtained by dividing the AOB angle by the OC beam, we can express through 4x.

Knowing that the degree value of the angle AOB is equal to 75 °, we will draw up an equation and determine what the angles BOC and AOC are equal to:

x + 4x = 75;

5x = 75;

x = 15;

4x = 4 * 15 = 60.

Answer: The degree value of the AOC angle is 15 °, and the degree value of the AOC angle is 60 °.