Question 621044
The formula for the sum of the interior angles (vertices) of a polygon is (n-2)180 where n is the number of sides, and must be a whole number.  A polygon has 3 or 4 or 5 or... some whole number of sides.<P>
A regular polygon has each vertex measure the sum of the interior angles ( (n-2)180) divided equally amongst the number of sides n:  {{{(n-2)180 / n}}}.<P>
Can this equal 110 when n is a whole number?<P>

{{{(n-2)180 / n = 110}}} | multiply both sides by n and distribute the 180<P>
180n - 360 = 110n  | Add 360 to both sides and subtract 110 n from both sides.<P>
70n = 360 so n = 360/70 = 36/7 - which isn't a whole number.  This polygon would have to have 5 and 1/7 sides.  That's not possible.
<P>Hope the solution helped.  Sometimes you need more than a solution.  Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)