Yes, it's true. The Inscribed Angle Theorem states that for any chord, the inscribed angle is 1/2 of the central angle. For example, in your diagram, angle KNL is 1/2 angle KOL. In your case angle KNL = 1/2 angle KOL = 1/4 angle KOM.
Also angle MNL = 1/2 angle MOL = 1/4 angle KOM.
The Inscribed Angle Theorem is a good theorem to add to your arsenal. A good discussion is found at wikapedia. This theorem is in Euclid's Elements.