Here is what I came up with using my basic understanding of algebra.
The angles for segments are taken from the outside edge rather than from the centre for good reason but they are related to the angle from the centre of a circle.
Without boring you with the maths this what I came up with
X is the number of segments
assume the angle of the segment is Y
eg. the angle for a 16 segment circle is as follows.
Y=90-(180/16) =90-11.25 =78.75 degrees
For 12 segments
Y=90-(180/12) =90-15 =75 degrees
If i’m wrong please let me know.
-- Grumpy - "Always look on the bright side of life"- Monty Python