<PRE><B>Question 760100</B>
SIDES___________TOTAL DEGREES
3_______________180
4_______________180*2
5_______________180*3
6_______________180*4
n_______________180(n-2)


You case indicates {{{(180(n-4))/(n-2)=144}}}.
You have 2*90 plus (n-4)*144 total degrees where n is also the count of the angles.  The 144 degree angles will sum to {{{144(n-2)}}} degrees.  You account for the triangles associated with these using {{{180(n-4)}}} degrees, because two OTHER angles are 90 degrees each.

15(n-4)=(n-2)12
5(n-4)=4(n-2)
5n-20=4n-8
n=20-8
n=12</PRE>