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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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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