SOLUTION: One angle of a polygon has 140 degrees and the rest are each 40 degrees smaller. Find the number of sides of the polygon.

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Question 597182: One angle of a polygon has 140 degrees and the rest are each 40 degrees smaller. Find the number of sides of the polygon.
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You have one angle of 140 degrees and (n - 1) angles of 100 degrees each. The sum of the interior angles of any n-gon is given by 180(n - 2)



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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One angle of a polygon has 140 degrees and the rest are each 40 degrees smaller. Find the number of sides of the polygon.
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If you mean the rest are each 100 degs:
Possible sums are:
340
440
540 --> 5 sides
640
.
.
.
1440 --> 10 sides
.
.
.
2340 --> 15 sides
etc
The sum has to be a multiple of 180. Adding 900 degs gives the results.