The new efficient numerical-analytical method of electromagnetic interior boundary value problem solving is presented with waveguide H plane angled bends as examples of implementation. The method essence consists in the analytical inversion of the main difference part of the initially derived ill-posed matrix equation of the first kind. As a result, the problem is reduced to the solution of the second-kind matrix equation with an invertible operator. The proposed method differs from other methods dealing with so-called modified Wiener-Hopf geometry structures. It is oriented to noncoordinate boundary value problems to which the ones of angular waveguide discontinuities are related. Detailed consideration of all parts of the numerical algorithm ensures its high efficiency. As application examples, the data for designing the matched truncated corners in a single-mode waveguide and the results of comparison of the known high-frequency heuristic estimations with the exact simulation of waveguide corners having a quasi-optical mirror are presented.