We investigate the properties of plasmon polaritons guided by 2D monoangular metal corners with a vector finite-element method. Such corner waveguides in general include both V-channel- and Λ-wedge-type waveguides. The influences of both geometric parameters (i.e., corner angle, tip sharpness, etc.) and operating wavelength to the mode properties, such as effective mode index, loss, and mode field size, are inspected. It is noticed that both a smaller corner angle and a sharper corner tip help to better confine the mode field. The confinement of the V-channel waveguide is found to be especially sensitive to its angle, while the confinement of the Λ-wedge waveguide is affected about equally by its angle and tip sharpness. Almost all superior mode field confinement is realized at the expense of higher propagation loss for such waveguides. The chromatic dispersion of such waveguides is found to be adequate for applications in integrated optical circuits. The mode behaviors of realistic corner waveguides with finite sidewalls are also studied.