The OM beam divided the angle CОК equal to 90 into two angles CОМ and MOK.

The OM beam divided the angle CОК equal to 90 into two angles CОМ and MOK. The СОМ angle is 2 3/5 times greater than the МОК angle. What are the angles COM and MOC equal to?

Let the angle MOC have a degree measure x °. Then, if it is known that the angle CОМ is 2 3/5 times greater than the angle MOK, then its value will be (2 3/5 * x) °. Because according to the condition of the problem, the angle CОК is equal to 90 °, and it consists precisely of the angles CОМ and MOK, then the following equality will be true:

x + 2 3 / 5x = 90,

3 3 / 5x = 90,

18 / 5x = 90

x = 90/18 * 5,

x = 25.

Accordingly, the angle СОМ will be equal to:

25 * 2 3/5 = 25 * 13/5 = 5 * 13 = 65 (°).

Answer: the MOC angle is 25 °, the COM angle is 65 °.