In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in ℂPn relative to a possibly degenerate set of hyperplanes. In this paper, we generalize Nochka's theorem to the case of curves in a complex projective variety intersecting hypersurfaces in subgeneral position. Further work will be needed to determine the optimal notion of subgeneral position under which this result can hold, and to lower the effective truncation level which we achieved.