The bisector OC and ray OM are drawn from the vertex of the unfolded angle EOK so that the angle COM = 33 degrees.

The bisector OC and ray OM are drawn from the vertex of the unfolded angle EOK so that the angle COM = 33 degrees. What is the degree measure of the EOM angle?

Since the beam OC is a bisector, the angles EOC and RNC are equal. Since the EOC angle is unfolded (that is, equal to 180 degrees), the EOC angle = the SOC angle = 180/2 = 90 degrees.
There may be 2 cases.
1) The OM beam is to the right of the OS bisector. Then the angle EOM is equal to the sum of the angles EOC and SOM.
ЕОМ = ЕОС + СОМ
Angle EOC = 90 degrees
SOM angle = 33 degrees (as required)
Then the angle EOM = 90 + 33 = 123 degrees
2) Beam OM is to the left of the OS bisector. Then the angle EOM is equal to the difference between the angles EOC and SOM
ЕОМ = ЕОС – СОМ
Angle EOC = 90 degrees
SOM angle = 33 degrees (as required)
Then the angle EOM = 90 – 33 = 57 degrees
Answer: The EOM angle can be 57 degrees or 123 degrees