Question about a proof theorem 5.2 of Humphreys

Question

I am reading through the proof of every semisimple Lie Algebra being a direct sum of simple ideals. Firstly, we take an arbitrary ideal $I$ and define $I^{\bot} = $ {$x \in L | \kappa(x,y) = 0 $ for all $ y \in I$}. Now I get why $I \cap I^{\bot} = 0$, but then Humphrey claims that dim $I$ + dim $I^{\bot}$ = dim $L$. I don't see why this is true?