# dimension of orthogonal complement

We know that if $$U$$ is a subspace of $$V$$ (finite-dimensional), then $$V = U oplus U^perp$$. Given this theorem, how does this lead to the conclusion that $$dim U^perp = dim V – dim U$$? This seems like a stupid question because it seems obvious, but I’m still unclear with this notion of a direct sum and the dimensions of subspaces adding up to the vector space.