What is the internal angle of a regular #17#-sided polygon?
A heptadecagon (
The internal angles of a (plane) triangle sum to
So the total sum of the internal angles of a heptadecagon is:
#15pi#radians #" "#or #" "15 * 180^@ = 2700^@#
So each interior angle in a regular heptadecagon is:
#2700^@/17 ~~ 158^@ 49' 24#"
As a result, the regular heptadecagon is one of the few prime sided figures constructable using an unmarked ruler and pair of compasses - that is using a classical construction.
A useful way to work with the angles in polygons is using the exterior angles.
The sum of the exterior angles of any polygon is always
In a regular polygon with
The interior angle
So, for a polygon with 17 sides,