SOLUTION: What are the angles and length of each side of a hexagon with diameter 36 inches?

   F ____E
    /\  /\
  A/__\/__\D
   \  /\  /
    \/__\/
    B    C

Now,AO=OD=1/2 of AD
Then AO=(1/2)36=18 inches
Similarly,AO=BO=CO=DO=EO=FO

For a polygon with 'n' sides,the exterior angle is given by the formula:

For a hexagon,exterior angle=360/6=60 degrees
Therefore the interior angle is given by:

Hence for a hexagon,interior angle is 180-60=120 degrees.

Therefore the angles for the hexagon is 120 degrees

Hence angle ABC=BCD=CDE and so on for all the angles for the hexagon.
Then angle ABO=angle OBC=half of angle ABC
So angle ABO=(1/2)120=60 degrees

Now look at triangle AOB

    O
    /\
   /  \
  A----B

Now the angle at the center O is 360 degrees,divided into 6 parts.
Hence each part is 60 degrees.
This means angle AOB=60 degrees

Then in triangle AOB,all three angles are 60 degrees.
It is an equilateral triangle with all equal angles,hence all its sides are also equal.
We know sides OA=OB.
Then side AB will also be equal to AO and OB
Therefore AB=18 inches.
This is the length of the side of the hexagon=18 inches

Angle=120 degrees,Side=18 inches

Hope this helps,
Prabhat