Question 752033: is it possible to draw a regular polygon with an interior angle of 115 degrees grade6 explanation
Answer by reviewermath(1029)   (Show Source):
You can put this solution on YOUR website! Q: is it possible to draw a regular polygon with an interior angle of 115 degrees grade6 explanation
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A:
If each interior angle of a regular polygon with n sides is 115°, then the sum of the interior angles is equal to 115n degrees.
In a polygon with n sides, the sum of the interior angles is 180(n - 2) degrees.
180(n - 2) = 115n
180n - 360 = 115n
65n = 360
n ≈ 5.538 (NOT a whole number)
If a polygon has n sides then, n must be a whole number greater than or equal to 3.
It is NOT possible to draw a regular polygon with an interior angle of 115 degrees because the computed value of n is NOT a whole number.
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