Question

If a regular polygon has 54 diagonals how many sides does it have?
What are the sums of the interior angles of the polygons?
What are the sums of the exterior angles of the polygons?
What is the measure of one interior angle?
What is the measure of one exterior angle?

Answer 1

Here is a calculator which can solve some of those questions:
http://www.1728.org/polygon.htm

Answer 2

Thanks!