What are the angles to a 5 pointed star?

Question

A hollow star like a starfish

Answer 1

Assuming that:
1.This star is equilateral.
2. All point angles are equal.
3. All obtuse angles are equal.

The inner obtuse angles are 108deg.
The outer point angles are 36deg.
.

Answer 2

each line making the star is the cord across 2/5 of a circle
the interior (central) angle subtended by this chord can be found:
l
let x be the interior angle
using arc length = theta (r)
a=xr or x=a/r

a line drawn from the center to each end of the cord forms an isoceles triangle with the angle x at the center.

The other two angles are equal to each other and equal to (pi-x)/2 and each angle is 1/ 2 of the angle of the point of the star.
therefore the angle at the point of the star =
pi-x in radians
EDITED:
now the arc length is 2/5 of the circumference =
(2/5)2pir=(4/5)pir
therefor x=a/r =(4/5)pir)/r=4pi/5i

the angle at each point is is pi -4pi/5 =36 deg

Answer 3

The angles can vary over some values and still give 5 pointed stars.