Thread: Polygon..

The interior angles of a polygon have measures 170 degrees, 160 degrees, 150 degrees, 140 degrees, ... down to some smallest angle. The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression. Find the number of sides of the polygon.

I don't know how to solve this. Please help.

if the interior angles are 170, 160, 150, ...

the exterior angles are 10, 20, 30, ...

the exterior angles of any polygon sum to 360 degrees.

Further, if by "The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression" you mean that all the angles are in an arithmetic progression, it follows that all exterior angles differ by 10: 10+ 20+ 30+ 40+ 50+ 60+ 70+ 80= 360. Now, how many sides are there?

oh there would have to be 8 sides because the exterior angles are 80, 70, 60, 50, 40, 30 , 20, and 10 --> which all add up to 360. And since the number of angles equals the # of sides there would have to be 8 sides.