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)   (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)   (Show Source): You can put this solution on YOUR website!

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

you can divide the polygon into identical 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 degrees and will be divided in identical angles that each must be 360/39 =9.23 degrees
than the other angles, from an interior angle of the polygon is made up, must be:
degrees
so, an interior angle of the sided polygon is degree


using the general formula for the measure of the interior angles of an
regular polygon which is you can arrive to same answer
so if we have interior angles of
degrees each

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