<PRE><B>Question 1118226</B>
&lt;br&gt;
The sum of the exterior angles of any polygon is 360 degrees.  So to find the measure of an exterior angle of a regular n-gon, divide 360 by n.  Then the interior angle is 180 minus the measure of the exterior angle.&lt;br&gt;
To see if a given integer angle measure x can be the measure of an interior angle of a polygon, subtract x from 180 and see if the result is a factor of 360.&lt;br&gt;
We can quickly rule out many of the given angle measures by finding the interior angle measure of a regular n-gon for small values of n:&lt;br&gt;
triangle (n=3): exterior angle 360/3 = 120; interior angle 180-120 = 60
square (n=4): exterior angle 360/4 90; interior angle 180=90 = 90
pentagon (n=5): exterior angle 360/5 = 72; interior angle 180-72 = 108
hexagon (n=6): exterior angle 360/6 = 60; interior angle 180-60 = 120&lt;br&gt;
So the four smallest interior angle measures for regular polygons are 60, 90, 108, and 120.  That rules out all the other numbers shown that are less than 120.&lt;br&gt;
It should be obvious that an interior angle of a regular polygon can&#39;t be 180 degrees or more.  If a polygon has an interior angle measure of more than 180 degrees, then the polygon is not convex&lt;br&gt;
That leaves only two more given numbers to check -- 144 and 150:&lt;br&gt;
interior angle 144; exterior angle 180-144 = 36; 360/10 = 36.  A regular polygon with 10 sides (decagon) has an interior angle of 144 degrees.
interior angle 150; exterior angle 180-150 = 30; 360/12 = 30.  A regular polygon with 12 sides (dodecagon) has an interior angle of 150 degrees.&lt;br&gt;
To summarize, then, and answer all your questions....&lt;br&gt;
An interior angle of 360 degrees makes no sense.
An interior angle of 210 or 240 degrees means the polygon is not convex and therefore cannot be regular.
If a triangle has an interior angle of 10, 15, 20, 30, 40, 45, 50, 72, 75, 80, or 100, then it cannot be a regular polygon.
The other angle measurements shown can be the interior angle measurements of a regular polygon:
60 degrees: equilateral triangle
90 degrees: square
108 degrees: regular pentagon
120 degrees: regular hexagon
144 degrees: regular decagon
150 degrees: regular dodecagon</PRE>