The anaphase-promoting complex/cyclosome (APC/C) regulates sister chromatid segregation and the exit from mitosis. Selection of most APC/C substrates is controlled by coactivator subunits (either Cdc20 or Cdh1) that interact with substrate destruction motifs—predominantly the destruction (D) box and KEN box degrons. How coactivators recognize D box degrons and how this is inhibited by APC/C regulatory proteins is not defined at the atomic level. Here, from the crystal structure of S. cerevisiae Cdh1 in complex with its specific inhibitor Acm1, which incorporates D and KEN box pseudosubstrate motifs, we describe the molecular basis for D box recognition. Additional interactions between Acm1 and Cdh1 identify a third protein-binding site on Cdh1 that is likely to confer coactivator-specific protein functions including substrate association. We provide a structural rationalization for D box and KEN box recognition by coactivators and demonstrate that many noncanonical APC/C degrons bind APC/C coactivators at the D box coreceptor.