SOLUTION: i have had trouble working on this math problem and i was wondering if someone could help me? Please and Thank you! I would deeply appreciate it! What is the ratio of the measur

Let's do the last one first:

The sum of the interior angles of any n-gon is given by



If the polygon is regular then all of its interior angles are equal in
measure, so each one of them must be that sum divided by n. So



The sum of the exterior angles of any n-gon is 360°

If the polygon is regular then all of its exterior angles are equal in
measure, so each one of them must be 360° divided by n. So



So the ratio of the measure of an interior angle to the measure of an 
exterior angle in a regular n-gon is






Invert the second fraction and change division to multiplication



Cnacel the n's and the 180° into the 360° getting 2 on the bottom:



A regular hexagon has 6 sides, so substitute n=6 in the equation:

 and the ratio is 2 to 1 or 2:1.

A regular decagon has 10 sides, so substitute n=10 in the equation:

 and the ratio is 4 to 1 or 4:1.

Edwin