  We study $W^{1,p}$ Lagrange interpolation error estimates for general
quadrilateral $\mathcal{Q}_{k}$ finite elements with $k\ge 2$. For the most
standard case of $p=2$ it turns out that the constant $C$ involved in the error
estimate can be bounded in terms of the minimal interior angle of the
quadrilateral. Moreover, the same holds for any $p$ in the range $1\le p<3$. On
the other hand, for $3\le p$ we show that $C$ also depends on the maximal
interior angle. We provide some counterexamples showing that our results are
sharp.
