<PRE><B>Question 1010975</B>
ratio of the sum of the interior angles to the sum of the exterior angles is 9/2.


i believe you want to find the number of sides in the regular polygon.


the sum of the exterior angles of a polygon is always 360.


the sum of the interior angles of a polygon is equal to (n-2)*180.


since the ratio of the sum of the interior angles of the polygon to the sum of the exterior angles of the polygon is 9/2, your formula would be:


9/2 = ((n-2)*180)/360


cross multiply to get:


9 * 360 = 2 * ((n-2)*180)


simplify to get:


3240 = 2 * (180*n-360)


simplify further to get:


3240 = 360*n-720


add 720 to both sides of this equation to get:


3960 = 360*n


divide both sides of this equation by 360 to get:


n = 11


if we did this correctly, the number of sides of the regular polygon is 11.


the sum of the exterior angles is 360.


the sum of the interior angles is (11-2)*180 = 9*180 = 1620


the ratio of the sum of the interior to the sum of the exterior becomes:


1620 / 360 which is equal to 9/2 if you divide both numerator and denominator by 180.


looks good.


you can also use the cross product to see if the ratios are the same.


9/2 = 1620/360


cross multiply to get 9*360 = 2*1620 which results in 3240 = 3240 which confirms the ratios are the same.








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