SOLUTION: how many sides has an equiangular polygon if one of its angles is 120? 150?

Question 804495: how many sides has an equiangular polygon if one of its angles is 120? 150?
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Use the formula for the sum of the angles, S, of an n-sided polygon given by
(1) S = 180*(n-2) degrees
You are given an n-sided regular polygon which means that the n angles are also equal. Then the sum of the n angles is n times the measure of the equal angles.
Then we have for the 120 degree angles
(2) 180*(n-2) = 120*n or
(3) 180*n - 360 = 120*n or
(4) (180-120)*n = 360 or
(5) 60*n = 360 or
(6) n = 6
Check this with (2).
Is (180*(6-2) = 6*120)?
Is (180*4 = 720)?
Is (720 = 720)? Yes
For n 150 degree angles we get
(7) 180*(n-2) = 150*n or
(8) 180*n - 360 = 150*n or
(9) (180-150)*n = 360 or
(10) 30*n = 360 or
(11) n = 12
Check this with (2).
Is (180*(12-2) = 12*150)?
Is (180*10 = 1800)?
Is (1800 = 1800)? Yes
Answer: the 120 degree polynomial has 6 sides and the 150 degree polynomial has 12 sides.

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