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In a regular polygon each interior angle is 120 deg. greater than each exterior angle....

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christiano-cr7 | Salutatorian

Posted July 16, 2013 at 5:33 AM via web

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In a regular polygon each interior angle is 120 deg. greater than each exterior angle. Calculate the number of legs of the polygon.

 

 

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

Posted July 16, 2013 at 5:43 AM (Answer #1)

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Let us say we have n legs in the polygon.

Sum of interior angles in the polygon `= (n-2)xx180`

 

If the interior angle is X then exterior angle would be `x-120` .

But at any point;

interior angle+exterior angle `= 180`

`x+x-120 = 180`

`2x = 300`

`x = 150`

 

Since we have n legs the sum of interior angles would be `150xxn` .

`(n-2)xx180 = 150xxn`

`n = 12`

 

So the polygon has 12 legs.

 

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