Question 777906: A regular polygon has 45 sides. What is the size of an interior angle?
Found 2 solutions by Cromlix, FrankM:
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! A 45 sided polygon has a sum
of angles = 43 * 180 = 7740 degrees.
a regular 45 side polygon has 45 equal
exterior angles whose sum is 7740.
So, each exterior angle = 7740/45 = 172 degrees.
At each vertex, interior angle + exterior angle
= 180 degrees.
Thus every interior angle = 180 - 172 = 8 degrees.
Hope this helps.
:-)
Answer by FrankM(1040)  (Show Source):
You can put this solution on YOUR website! In your mind, find the center of this polygon. A line is drawn from center to every vertex, 45 lines radiating out. 360/45 is 8 degrees, right? So each triangle you made has one 8 degree angle.
180-8=172 which is the answer you seek.
Now 172 is the total of the other 2 angles, so half is 86, but it takes two to form the full angle you are measuring. The above approach can easily be followed for any N sided polygon.
(Note - 8 is the small angle of the imaginary triangle in your figure. The polygon itself has 45 sides, and 8 degrees doesn't appear until we go through the thought process to solve the problem, it's there as an intermediate step only.)
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