It is known that the angle MOK = angle NOL = 144 degrees. determine if these corners are adjacent or vertical.

From the condition of the problem, it is known that the angle MOC is equal to the angle NOL and each of them is equal to 144 degrees. Adjacent corners and vertical corners are formed when two straight lines intersect. The sum of adjacent angles is 180 degrees. The vertical angles are equal to each other. Since the sum of the data in specifying the angles (144 + 144 = 288 degrees) is greater than 180 degrees, these angles cannot be adjacent. The MOC angle is equal to the NOL angle equal to 144 degrees, that is, these angles are vertical.
Answer: Angle MOK and angle NOL are vertical.