SOLUTION: can a regular polygon have an interior angle of 157 degrees ?

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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