Question 162277: What is the size of each interior angle of a regular polygon if the number of sides is 4? 5? 6? 7? 8? 9?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! What is the size of each interior angle of a regular polygon if the number of sides is 4? 5? 6? 7? 8? 9?
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The number of sides is the same as the number of angles and vertices.
The total of the interior angles of a polygon is 180*(n-2), where n is the number of sides, angles and vertices.
For regular polygons, all angles are equal, so they're the total/n.
That is 180*(n-2)/n
Just sub the number for n:
For 4, it's 360/4 = 90 degs
For 5, it's 540/5 = 108 degs
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For 9, it's 1260/9 = 140 degs
For 36, it's 6120/36 = 170 degs
Notice that the angle increase as the number of sides increase. You can use that as a check for polygons with 5, 6, 7 & 8 sides.
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For 1000, it's 179.64 degs
As n approaches infinity (which is a circle), the angle approaches 180 degs.
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