First solution (shortcut):

The star doesn't contain any particular size or restriction. Therefore, the sum of all 5 angles is the same for any star. Let's choose a symmetric star for which all 5 angles are equal, . The star can be circumscribed as shown in the figure.

Because the central angle () is twice as large as the inscribed angle () and 5 central angles cover a whole circle ():



Strategy

If a geometric figure doesn't contain any particular size or restriction and there is a property that holds for any geometric figure of a certain type, you can choose the simplest figure to solve the problem faster.

Useful formulas:

If ⌒AC is an arc of a circle, for any point on the circle, ∠ABC (an inscribed angle) is exactly half ∠AOC (a central angle).