Question 569498
I know your frustration. It's hard to figure out one's own mistake, and it is obvious that a polygon could not have -0.25 sides.
 {{{(n-2)180/n}}} would be the measure of one angle in a regular n-sided polygon. That's probably what you were thinking of, but the problem refers to the sum of the measures of the angles.
The  sum of the measures of the vertex angles of an n-sided polygon is {{{(n-2)180}}}.
If {{{(n-2)180=1620}}} --> {{{n-2=1620/180}}} --> {{{n-2=9}}} --> {{{n=9+2}}} --> {{{highlight(n=11)}}}