Question 966148: Prove that the exterior angle of a regular decagon is one - third the interior angle of a regular Pentagon.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the exterior angle of a decagon is equal to 360/10 = 36 degrees.
the internal angle of a pentagon is equal to 180 - 360/5 which is equal to 180 - 72 degrees which is equal to 108 degrees.
3 * 36 is equal to 108 degrees.
the exterior angle of a decagon is equal to 1/3 the interior angle of a pentagon.
these are all regular polygons, by the way.
the formulas only work with regular polygons.
the exterior angle of a pentagon is equal to 360/n, where n is the number of siges.
the interior angle of a polygon can be found by either one of the following formulas:
interior angle = (n-2) * 180 / n
interior angle = 180 - exterior angle.
for the pentagon, the first formula will become 3 * 180 / 5 = 3 * 36 = 108.
for the pentagon, the second formula will becomes 180 - 360/5 = 180 - 72 = 108.
you can take your pick as to which one is easier to work with.
from my perspective, the exterior angle formula is easier to remember.
exterior angle = 360 / n.
the interior angle of a polygon is always supplementary to the exterior angle of the same polygon.
interior angle = 180 - exterior angle.
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