If you want to construct a Star-shaped Polygon with 6 points with point angles of 30o, what should be the dent angle?
a star polygon with n points and point angle, X, has a dent angle of:
dent angle = (360/n) + X
therefore, in your question, n=6 and X=30:
dent angle = (360/6) + 30 = 90
source:
teach.valdosta.edu/plmoch/MATH3162/Spring%202009/11-3.pdf