Question 233660: can a regular polygon have an interior angle of 157 degrees ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I think no.
the formula is:
degrees of each angle = (n-2) * 180 / n
Let d = degrees of the angle.
d = (n-2) * 180 / n
Multiply both sides by n to get:
d*n = (n-2) * 180
Remove Parentheses to get:
d*n = 180*n - 360
Subtract d*n from both sides and add 360 to both sides to get:
180*n - d*n = 360
Factor out the n to get:
(180-d)*n = 360
Divide both sides by (180-d) to get:
n = 360 / (180-d)
360 / (180-d) has to be an integer.
If d = 157, then:
n = 360 / (180-157) becomes:
n = 360 / 23 which becomes:
n = 15.65..... which is not an integer.
The answer is no because n is not an integer as it needs to be.
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