Question 236449
For any n-gon (ie a polygon with 'n' sides), the sum of the interior angles can be found by {{{S=180(n-2)}}}. Divide this sum by the number of sides 'n' to get {{{(180(n-2))/n}}} which is the measure of a single interior angle. 



Since the measure of each interior angle is 165 degrees, this means that {{{(180(n-2))/n=165}}} 



{{{(180(n-2))/n=165}}} Start with the given equation.



{{{180(n-2)=165n}}} Multiply both sides by 'n'.



{{{180n-360=165n}}} Distribute.



{{{180n=165n+360}}} Add {{{360}}} to both sides.



{{{180n-165n=360}}} Subtract {{{165n}}} from both sides.



{{{15n=360}}} Combine like terms on the left side.



{{{n=(360)/(15)}}} Divide both sides by {{{15}}} to isolate {{{n}}}.



{{{n=24}}} Reduce.



So the polygon has 24 sides.