<PRE><B>Question 966148</B>
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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