SOLUTION: describe the relationship between no sides of a regular polygon and the measure of each angle

Each central angle is equal to   radians,  or   degrees.


Each interior angle is equal to    radians,  or    degrees.


Or, in more familiar form, each interior angle is equal to    degrees.

Any n-sided polygon has n sides, n vertices and n interior angles.
Pick any one of the n vertices.  The 2 vertices adjacent to that vertex 
make up 2 of the n sides.  If we join the chosen vertex to each of the 
other n-2 vertices we will have n-2 triangles and the sum of all their 
angles will give us (n-2)∙180° for the sum of all the n interior angles 
of the polygon. 

Now in a regular polygon all the angles are equal, so each angle will
measure 1/nth of the sum (n-2)∙180°, or



That is the answer AND WHY!

Edwin