In rotational resonance, a solid-state NMR technique for measuring dipolar couplings, the spinning speed, upsilon(r), is adjusted such that Delta nu(iso) = n upsilon(r) where Delta nu(iso) is isotropic chemical shifts difference and n (an integer) is referred to as the order. At higher orders of the rotational resonance the magnetization exchange rate depends strongly upon the relative orientations of the two carbons, particularly if both sites have broad chemical shift anisotropy. Experimental exchange curves and computer simulations for crystalline [C-13(2)]glycolic acid at n = 4 demonstrate that this effect can be used to measure dihedral angles. Pur data indicate that the hydroxyl group and the two carboxyl oxygen atoms are in the same plane, in agreement with crystallography. Phosphoglycolic acid (PGA) is a transition-state analog inhibitor of triose phosphate isomerase (TIM). The n = 4 exchange curves for [C-13(2)]PGA bound to TIM indicate an "in-plane" conformation for the phosphate with respect to the carboxy group. This conformation had been previously proposed to explain the lack of phosphate elimination during catalysis and had been suggested also on the basis of crystallographic results. The chemical shift anisotropy of the carboxy group of PGA indicates that it is deprotonated when bound to the enzyme. We discuss the scope of applications of rotational resonance for measuring dihedral angles in other systems.