In triangle MKO, MK = OK (radii), so it's isosceles. Angle MKO = 90 degrees because MK is a chord and ON is a diameter, and the angle subtended by a diameter at any point on the circumference is 90 degrees. Thus, triangle MKO is a right-angled isosceles triangle. Therefore, angle KMO = angle MOK = 45 degrees. Since angle MOK = x, x = 45 degrees.