jmc

The seven points divide the circumference of the circle into seven equal small arcs each with measure $\frac{360^{\circ }}{7}$.

$\angle ACE$ cuts off a minor arc $\widehat{AE}$, which consists of three small arcs and thus $$\widehat{AE}=3\cdot \frac{360^{\circ }}{7}.$$It follows that $$\angle ACE=3\cdot \frac{360^{\circ }}{7}\cdot \frac{1}{2}=\frac{3\cdot 180^{\circ }}{7}.$$Each tip of the star is formed by an angle which cuts off three small arcs in a similar fashion. Thus each tip of the star measures $\frac{3\cdot 180^{\circ }}{7}$ and hence all seven tips of the star together measure $3\cdot 180^{\circ }=\boxed{540}$ degrees.