In this work we study the problem of diffraction of an acoustic plane wave by a plane angular sector with the Dirichlet boundary condition on its surface. By means of incomplete separation of variables, with the aid of Watson–Bessel integral representation the problem is reduced to an infinite system of linear summation equations of the second kind. Exploiting the reduction of the integral representation to that of the Sommerfeld type, a consequent procedure is then developed in order to describe different components in the far field asymptotics. To that end, the analytic properties and singularities of the integrand in the Sommerfeld integral are carefully studied. The latter plays a crucial role when evaluating the Sommerfeld integral by means of the saddle point technique because these singularities are captured in the process of deformation of the Sommerfeld contours into the steepest descent paths. The corresponding asymptotic contributions of the singularities lead to the description of the different ty