SOLUTION: find the number of sides in a regular polygon that has an interior angle of 165.5? with an explaination please .

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Question 457554: find the number of sides in a regular polygon that has an interior angle of 165.5?
with an explaination please .
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the interior angle of a regular polygon is:


x=%28180%28n-2%29%29%2Fn where 'x' is the measure of the interior angle and 'n' is the number of sides of the polygon.


In this case, we know that "a regular polygon that has an interior angle of 165.5", so x=165.5. Plug this in to get


165.5=%28180%28n-2%29%29%2Fn



Now solve for 'n'


165.5n=180%28n-2%29


165.5n=180n-360


165.5n-180n=-360


-14.5n=-360


n=-360%2F%28-14.5%29


n=24.8275862068966


Round to the nearest whole number to get n=25



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I'm thinking there's a typo and the interior angle should be 165.


If so, then...


x=%28180%28n-2%29%29%2Fn


165=%28180%28n-2%29%29%2Fn


165n=180%28n-2%29


165n=180n-360


165n-180n=-360


-15n=-360


n=-360%2F%28-15%29


n=24


So if the actual interior angle is 165 degrees, then there are 24 sides.