The CP29 light harvesting complex from green plants is a pigment-protein complex believed to collect, conduct, and quench electronic excitation energy in photosynthesis. We have spectroscopically determined the relative angle between electronic transition dipole moments of its chlorophyll excitation energy transfer pairs in their local protein environments without relying on simulations or an X-ray crystal structure. To do so, we measure a basis set of polarized 2D electronic spectra and isolate their absorptive components on account of the tensor relation between the light polarization sequences used to obtain them. This broadly applicable advance further enhances the acuity of polarized 2D electronic spectroscopy and provides a general means to initiate or feed back on the structural modeling of electronically-coupled chromophores in condensed phase systems, tightening the inferred relations between the spatial and electronic landscapes of ultrafast energy flow. We also discuss the pigment composition of CP29 in the context of light harvesting, energy channeling, and photoprotection within photosystem II.