To construct a 15-sided polygon:
Construct a pentagon inscribed in a circle.
Mark off a 72 angle by using two adjacent
vertices of the pentagon and connecting
each to the point at the center of the circle.
L
A
Bisect the angle until you have constructed
an angle measuring 9. The original 72
angle and the 9 angle should share a ray.
Using one ray of the 9 angle, construct an
equilateral triangle using the circle’s radius
as one side. This construction creates a
60angle along the ray of the 9 angle.
B
Bisect the 60 angle to create a 15 angle
along the ray of the 9 angle. Now a 24
angle exists that can be used to construct
the 15-gon. (The measurement of a circle is
360. If 360 is divided by 24, the quotient is
15.)
Reflect this angle around the circle to
create fifteen 24 angles.
Connect the points along the circle’s edge
to construct the sides of the 15-gon.