document.write( "Question 33843: find the no of sides of regular convex polygon whose angle is 40 deg?
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Algebra.Com's Answer #20242 by Earlsdon(6294) $\"\"$ $\"About$

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The measure of one vertex angle of a regular polygon is given by:
\n" ); document.write( " $\"%28n-2%29180%2Fn\"$ where n is the number of sides of the regular polygon...and, of course, it goes without saying, that n must be an integer >2(i.e, 3, 4, 5, 6, ...).
\n" ); document.write( "If the measure of one vertex angle of a regular polygon is 40 degrees, then we can write:
\n" ); document.write( " $\"%28n-2%29180%2Fn+=+40\"$ Simplify and solve for n.
\n" ); document.write( " $\"%28180n-360%29%2Fn+=+40\"$ Multiply both sides by n.
\n" ); document.write( " $\"180n+-+360+=+40n\"$ Add 360 to both sides.
\n" ); document.write( " $\"180n+=+360%2B40n\"$ Subtract 40n from both sides.
\n" ); document.write( " $\"140n+=+360\"$ Divide both sides by 140.
\n" ); document.write( " $\"n+=+2.57\"$ This is not possible since a regular polygon must have an integral numer of sides.\r
\n" ); document.write( "\n" ); document.write( "Conclusion:
\n" ); document.write( "There is no regular polygon whose vertex angle is 40 degrees. \n" ); document.write( "

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