In core-level electron energy loss spectroscopy (EELS) for anisotropic systems, the applied electric field is determined by the momentum transfer vector q, therefore the collection solid angle range for the scattering electrons and sample orientation will affect the measured EELS spectra.. Using the spatially resolved C 1s core excitation in carbon nanotube as an example, we show that the EELS measurement can be understood by a simple dipole theory of anisotropic core loss spectroscopy which decomposes the spectral contribution in terms of orientationelly averaged isotropic spectrum and linear dichrotic spectrum. In addition, we point out the Magic Angle (MA) conditions that allow the direct determination of the averaged spectra acquired independent of the exact sample orientation.