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
60angle 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.
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