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As you may recall, the sum of the interior angles of a triangle is 180 degHow many...

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christiano-cr7 | Salutatorian

Posted September 21, 2013 at 6:09 AM via web

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As you may recall, the sum of the interior angles of a triangle is 180 deg
How many sides must a polygon have if the sum of the interior angles is
2520 deg

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 21, 2013 at 6:14 AM (Answer #1)

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We know that if a polygon has n numbers of sides then we can form (n-2) triangles inside the polygon. In other words the sum of n interior angles are denoted by the sum of interior angles of (n-2) triangles.

So if the polygon has n sides;

`(n-2)xx180 = 2520`

`n-2 = 14`

`n = 16`

So the polygon has 16 sides.

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