Large changes in the magnetization of ferromagnetic films can be electrically driven by non-180 ferroelectric domain switching in underlying substrates, but the shear components of the strains that mediate these magnetoelectric effects have not been considered so far. Here we reveal the presence of these shear strains in a polycrystalline film of Ni on a 0.68Pb(Mg 1/3 Nb 2/3)O 3-0.32PbTiO 3 substrate in the pseudo-cubic (011) pc orientation. Although vibrating sample magnetometry records giant magnetoelectric effects that are consistent with the hitherto expected 90 rotations of a global magnetic easy axis, high-resolution vector maps of magnetization (constructed from photoemission electron microscopy data, with contrast from x-ray magnetic circular dichroism) reveal that the local magnetization typically rotates through smaller angles of 62-84. This shortfall with respect to 90 is a consequence of the shear strain associated with ferroelectric domain switching. The non-orthogonality represents both a challenge and an opportunity for the development and miniaturization of magnetoelectric devices. Wisconsin-Madison (J.-M. H.). D. P. acknowledges funding from the Agència de Gestió d'Ajuts Universitaris i de Recercaa-Generalitat de Catalunya (Grant 2014 BP-A 00079). We thank Diamond Light Source for time on beamline I06 (proposal SI-8876), and we thank Sen Zhang for discussions. Author contributions M.G. initiated the study. M.G. and N.D.M. led the project with S.S.D. R.M., R.P.C. and C.H.W.B. were responsible for the growth of thin film Ni. The collection and preliminary analysis of PEEM data were performed by M.G., with assistance from X.M., L.C.P and W.Y. All other experimental work was performed by M.G. F.M. and S.S.D. were responsible for constructing PEEM vector maps, and the subsequent pixel by pixel analysis. D.P. performed image and data processing. N.D.M. proposed the pixel-by-pixel analysis of PEEM vector maps that led to the key finding of sub 90° magnetization rotation. J. M.H. identified and calculated the shear strain that accompanies ferroelectric domain switching in PMN-PT. M.G. identified the resulting principal axes of strain and hence magnetic easy axes. M.G. and N.D.M. interpreted the observed magnetoelectric effects.