SOLUTION: can you please help me? I don't know what to do # of sides=? measure of each exterior angle=? measure of each interior angle-165 i know to find the interior angle you do 18

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Question 236449: can you please help me? I don't know what to do
# of sides=?
measure of each exterior angle=?
measure of each interior angle-165
i know to find the interior angle you do 180(n-2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For any n-gon (ie a polygon with 'n' sides), the sum of the interior angles can be found by S=180%28n-2%29. Divide this sum by the number of sides 'n' to get %28180%28n-2%29%29%2Fn which is the measure of a single interior angle.


Since the measure of each interior angle is 165 degrees, this means that %28180%28n-2%29%29%2Fn=165


%28180%28n-2%29%29%2Fn=165 Start with the given equation.


180%28n-2%29=165n Multiply both sides by 'n'.


180n-360=165n Distribute.


180n=165n%2B360 Add 360 to both sides.


180n-165n=360 Subtract 165n from both sides.


15n=360 Combine like terms on the left side.


n=%28360%29%2F%2815%29 Divide both sides by 15 to isolate n.


n=24 Reduce.


So the polygon has 24 sides.