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The sum of the interior angles of a polygon is 9x³. If x is 3 greater than the number of sides of the polygon, how many sides does the polygon have?

1 Answer

4 votes

Answer:

n = 7

Explanation:

The sum of the interior angles of a polygon is 9
x^2. If x is 3 greater than the number of sides of the polygon, how many sides does the polygon have?

The sum of the interior angles of a concave polygon can be found using the formula S = (n - 2)*180.

n= number of sides of the polygon

n-2 * 180 = the sum of the interior angles

9
x^2= the sum of the interior angles

9
x^2= (n-2) *180

x= 3+ n

9
(3+n)^(2)=(n-2) *180

9 (9+6n+n^2) = (n-2) *180

81+54n+9n^2 = (n-2) *180

n = 7

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