Question

A graphics designer wants to use a star-shaped polygon
with 10 points and a point angle of 12 degrees. What should be
the dent angle of this polygon?

Answer 1

if you are traveling along the leg of the star, the deflection angle is the angle you have to turn to get to the next leg.
d = deflection angle at a point
= 180 - 12 = 168
since there are points, the total point deflection angle at the points is 1680.
x = dent angle = 180+y
y = deflection angle at dent
To end where you start, you must have a total deflection of 360 degrees so,
360 = 1680 + 10y
reducing this,
y = -132
so x = 48 degrees