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Scattering of electromagnetic wave is considered for a composite structure consisting of an infinite dihedral wedge that is co-axially coupled with a dielectric covered slotted cylinder. The boundary-value method is employed using completeness property of the angular functions in the respective intervals. Problem is reduced to solution of system of algebraic equations of the second kind for the unknown coefficients of Fourier expansion of the scattered field. Analytical solution is obtained for certain value of cylinder slot-width. Scattered far-field and back radar cross section (BRCS) of the structure are evaluated asymptotically. The scattered field characteristics are also analyzed numerically with controlled precision. BRCS and the normalized radiation patterns of scattered field of narrow wedge for certain values of cylinder slot-width and electrical diameter of the cylinder are given.