I am currently studying Algebraic Geometry, and the wikipedia page of Fano Variety says the following "a smooth complete intersection of hypersurfaces in n-dimensional projective space is Fano if and only if the sum of their degrees is at most n".
I wonder how this statement can be proved. A fano variety is one which $-K_X$ is ample, where $X$ is a smooth projective variety and $K_X$ is the canonical divisor. I have already computed that $K_X=\mathfrak{O}_X(\sum d_i-n-1)$, where $d_i$ are the degree of the hypersurfaces. How should I use this to prove the statement regarding $X$ being Fano? Thanks in advance.