SOLUTION: You are given the measure of each interior angle of a regular n-gon. Find the value of n. 12.) 128 4/7 degrees i know you must use the formula n x (n-2) x 180

Question 133460: You are given the measure of each interior angle of a regular n-gon. Find the value of n.
12.) 128 4/7 degrees

i know you must use the formula
n x (n-2) x 180
---------------
n

but Im not sure what to do from here...
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Actually, you have an extra factor of n in the numerator of your formula. The formula for the measure of the interior angles of a regular n-sided polygon is:

.

Since you are given that the measure of the interior angle of your regular polygon is 128 4/7 degrees, you need to set your formula equal to this measure and then solve for n. Just as a sanity check, since the denominator of the fraction in the angular measure is 7, I expect that the number of sides will turn out to be 7 or some multiple of 7.

Multiply both sides by n:
(I added the whole number part of the angle measure and the fractional part because this formula system won't render mixed numbers)

Distribute:

Put the variable terms on the left, and the constants on the right:

Rather than converting everything to fractions, just multiply both sides by the denominator of 7:

, as suspected.
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