SOLUTION: In a regular polygon with N side each interior angle is 180 dgrees minus 360dgrees divided by N. How many sides does a polygon have if each interior angle is 150 dgree.

Question 59550: In a regular polygon with N side each interior angle is 180 dgrees minus 360dgrees divided by N. How many sides does a polygon have if each interior angle is 150 dgree.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
In a regular polygon with N side each interior angle is 180 dgrees minus 360dgrees divided by N. How many sides does a polygon have if each interior angle is 150 dgree.
YOU MEAN 180 - (360/N)
SUM OF ALL INTERIOR ANGLES IN A N SIDED POLYGON = (2N-4)*90 DEGREES
IF IT IS A REGULAR POLYGON THEN ALL N ANGLES ARE EQUAL AND HENCE EACH ANGLE =
[(2N-4)*90]/N DEGREES = 180 - (360/N)
150 = 180 - (360/N)
360/N = 180-150 =30
30N = 360
N=360/30 =12
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