SOrry for the very specific question, but curiosity bites....

So here's the story: an idecomposable principally polarized abelian surface is embedded in $P^8=|3\Theta |^* $ as a deg 18 surface A. Moreover $|3\Theta|^*$ decomposes into two eigenspaces w.r.t. the canonical involution: one $P^3$ and one $P^4$. The $P^3$ is a sublinear system with base points the 10 even 2-torsion points, whereas the $P^4$ has the 6 odd 2-torsion points as base points. On the other hand $P^3\cap A \subset P^8=$ 6 odd 2-tors points and $P^4\cap A \subset P^8=$ 10 even 2-torsion pts. It is known that the projections of A on the $P^3$ and $P^4$ are, respectively, a quartic 6-nodal K3 surface, and a sextic 10-nodal K3 in $P^4$.

Now from a trivial degree computation I see that the degree of both projections is two, can you see an easy direct way to show that it is indeed two?