Question 133460
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:


{{{((n-2)*180)/n}}}.


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.


{{{((n-2)*180)/n=128+4/7}}}


Multiply both sides by n:
{{{((n-2)*180)=n(128+4/7)}}} (I added the whole number part of the angle measure and the fractional part because this formula system won't render mixed numbers)


Distribute:
{{{180n-360=128n+4n/7}}}


Put the variable terms on the left, and the constants on the right:
{{{180n-128n-4n/7=360}}}


Rather than converting everything to fractions, just multiply both sides by the denominator of 7:
{{{1260n-896n-4n=2520}}}


{{{360n=2520}}}


{{{n=7}}}, as suspected.