SOLUTION: The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the numb

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Question 1203147: The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
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The sum of the interior angles of two regular polygons is 2520°.
If the number of sides of one of the polygons is 3 less than twice the number
of sides of the other, find the number of sides of each of the polygons.
~~~~~~~~~~~~~~~~~~ 

Let n be the number of sides of the "other" polygon.
Then the number of sides of the "one" polygon is (2n-3).


The sum of the interior angles of the "other" polygon is 180*(n-2) degrees.
The sum of the interior angles of the "one"   polygon is 180*((2n-3)-2)) = 180*(2n-5) degrees.


The sum of the interior angles of both polygons is

    180*(n-2) + 180*(2n-5) = 2520.


Simplify and find n.  First divide the terms of the equation by 180

    (n-2) + (2n-5) = 2520/180 = 14

    3n - 7 = 14

    3n = 14 + 7 = 21

     n = 21/3 = 7.


ANSWER.  One polygon is a regular seven-sided polygon (septagon). 
         The other polygon is a regular 2*7-3 = 11-gon.

Solved, with complete explanations.



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