We studied the effects of relative orientation of bowtie nanostructures on the plasmon resonance both experimentally and theoretically in this work. Specifically, we fabricated gold bowtie nanoantennas with rotated nanoprisms, measured the near-field and the far-field resonance behaviors using Raman spectroscopy and scattering microspectroscopy, and simulated the effects of the rotation angle on the localized surface plasmonic resonance using finite-difference time-domain simulations. In addition to the widely-discussed dipolar resonance in regular bowtie nanostructures, defined as tip-mode resonance in the present study, the excitations of edge-mode resonance were discovered under certain rotation angles of nanoprisms. Because of the resonances of different modes at different wavelengths, two different incident laser sources were used to measure the Raman spectra to provide evidence for the evolution of different resonance modes. Also, both the tip-mode and edge-mode resonances were verified by the simulated charge density distribution and their trends were discussed. Based on the discovered trend, a plasmon protractor was created with a near-exponential decay relationship between the relative resonance wavelength shift and cosine of the rotation angle. A plasmon hybridization model was also proposed for rotated bowties to explain the coupling between nanoprisms during rotation.