From the vertex of the unfolded angle EOK, the bisector OC and the ray

From the vertex of the unfolded angle EOK, the bisector OC and the ray OM are drawn so that СОМ = 33 *. What can be the degree measure of EOM?

An unfolded angle if all three points lie on the same straight line. The degree measure of such an angle is 180. angle EOK = 180 degrees. CO bisector, i.e. beam bisecting the angle.
Angle EOC = angle COK = 90.
We are not told where the OM beam is, so we analyze two possible options.
If the beam ОМ cuts the angle СОК, then the angle ЕОМ = angle ЕОС + angle СОМ = 90 + 33 = 123 degrees.
If the beam OM passes between the sides of the EO and the OC of the EOC angle, then the EOM angle = EOC angle – the COM angle = 90-33 = 57 degrees.
Answer: 123 degrees or 57 degrees.