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

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) (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(13215) (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).

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.

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