Calculate the number of times an angle must be repeated for it to complete a full rotation and for it to close

Calculate the number of times an angle must be repeated for it to complete
a full rotation and for it to close

I'm trying to calculate the number of times an angle must be repeated to
make a full rotation and become closed.
Example: The internal angle of a pentagon is 108 degrees and it must
repeat 5 times to complete a rotation and it closes at 540 degrees. It
closes a 540 degrees because that's when all the sides meet and close.
http://www.mathsisfun.com/geometry/interior-angles-polygons.html
How can I calculate these numbers for arbitrary angles like 72 degrees or
117 degrees, etc..
Does anyone know of a way to calculate this
Ps: I'm using matlab/octave thanks