Question 461249
The sum of the interior angles of a regular polygon with n angles is

{{{(n-2)180}}}. Since the angle of our polygon measure 156 degree, then the sum 

of interior angles is: {{{n*156}}}. Equalizing these two expressions for the sum 

of interior angles we have:{{{(n-2)*180=n*156}}}, solving this equation we get:

{{{180n-156n=360}}} => {{{24n=360}}} => {{{n=15}}}.

Answer:The number of sides of our polygon are 15.