SOLUTION: A polygon of n sides has half of the interior angles as 150 degrees each and the rest 170 degrees each. Find the value of n

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Question 1155788: A polygon of n sides has half of the interior angles as 150 degrees each and the rest 170 degrees each. Find the value of n
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A polygon of n sides has half of the interior angles as 150 degrees each and the rest 170 degrees each. Find the value of n
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Ext angles are 30 and 10, equal # of each
n = 2*360/(30+10) = 18 sides
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9*150 + 9*170 = 2880 degs interior sum
2880 = 180*(18 - 2) as a check

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) using interior angles....

The sum of the interior angles of a polygon with n sides is 180(n-2).

%28n%2F2%29170%2B%28n%2F2%29150+=+180%28n-2%29
%28n%2F2%29320+=+180n-360
160n+=+180n-360
20n+=+360
n+=+18

ANSWER: 18 sides

(2) using exterior angles....

Nearly always, a problem like this is easier to solve using the exterior angles, whose sum is always 360.

There are (n/2) exterior angles of 30 degrees and (n/2) of 10 degrees.

%28n%2F2%2930%2B%28n%2F2%2910+=+360
20n+=+360
n+=+18