We consider scattering of a scalar complex source beam (CSB) by wide-angle cones. We derive an asymptotic solution that consists of a complex geometrical optics term augmented by complex tip diffraction, expressed as a local spectral integral. The results are compared to the exact solution, expressed as a complex conical-harmonics expansion. It is shown that unlike the narrow-cone case, considered by us in an earlier publication, scattering by a wide cone is dominated not only by tip diffraction but also by beam reflection expressed by complex rays.