SOLUTION: A regular polygon has 39 sides. find the size of each interior angle. (could you explain the answer full as possible?)

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Question 689389: A regular polygon has 39 sides. find the size of each interior angle. (could you explain the answer full as possible?)

Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the interior angles of any -gon is given by



If the polygon is regular, then the measure of each interior angle is that total divided by .

Calculate:



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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
a regular polygon has 39 sides
to find: the size of each interior angle

you can divide the polygon into 39 identical isosceles triangles where two sides equal to radius of a circle circumscribed around the polygon.
so, the central angle at the center of the polygon is 360 degrees and will be divided in 39 identical angles that each must be 360/39 =9.23 degrees
than the other 2+ angles, from an interior angle of the polygon is made up, must be:
180+-+9.23+=+170.77 degrees
so, an interior angle of the 39 sided polygon is 170.77 degree


using the general formula for the measure of the interior angles of an n-sided
regular polygon which is %28%28n+-+2%29%2Fn%29+%2A+180 you can arrive to same answer
so if n+=+39 we have interior angles of
%28%2839+-+2%29%2F39%29%2A180+=+%2837%2F39%29%2A180+=0.94872+%2A180=170.7696=+170.77+degrees each