SOLUTION: 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,

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Question 174420: 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 numbers of an Arithmetic Progression. Find the number of sides of the polygon.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
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 numbers of an Arithmetic Progression. Find the number of sides of the polygon. 

First term = , difference = 

Formula for the sum of the first n terms:



Formula for the sum of the interior angles of an 
n-sided polygon:



Set the right sides of the formulas equal:







Multiply both sides by 2:



Distribute:



Combine like terms:



Get 0 on the right:



Rearrange in descending order:



Divide through by -10:



Factor left side:



Use zero-factor property:

   

Discard the negative answer.

It's an 8-sided polygon, or octagon.

Edwin
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