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

Question

Accepted Answer

The sum of the interior angles of a polygon is equal to 180(s – 2), where s is the number of sides of the polygon. Since the number of sides is three less than x and the sum of the interior angles is 9x 2 , 180(x – 3 – 2) = 9x 2 , 180x – 900 = 9x 2 , 9x 2 – 180x + 900 = 0, x 2 – 20x + 100 = 0, (x – 10)(x – 10) = 0, x = 10. Therefore, the number of sides of the polygon is (10) – 3 = 7 sides.

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