△GCE, from the external angle theorem, we get ∠1= ∠ c+∠ e.

Similarly, ∠ 2 = ∠ B+∠ D.

△AGH, which is derived from the theorem of sum of internal angles.

∠A+∠ 1+∠2= 180？

∴∠A+∠B+∠C+∠D+∠E= 180？

The sum of the five angles of the five-pointed star is 180 degrees.