document.write( "Question 408195: The measure of an interior angle of a regular polygon is three (3) times the measure of the exterior angle. How many sides does the polygon have? Is there a formula or something that needs to be used? \n" ); document.write( "
Algebra.Com's Answer #287697 by richard1234(7193)\"\" \"About 
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Let \"theta\" be the measure of the exterior angle, and \"3%2Atheta\" be the measure of the interior angle. These two must add to 180 degree (since they're a linear pair) so\r
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\n" ); document.write( "\n" ); document.write( "\"theta+%2B+3%2Atheta+=+180\" --> \"theta+=+45\", \"3%2Atheta\" = 135.\r
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\n" ); document.write( "\n" ); document.write( "Two ways to find the number of sides:\r
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\n" ); document.write( "\n" ); document.write( "Solution 1:
\n" ); document.write( "If you know that the sum of the exterior angles of an n-gon is 360 degrees, and that in this case the exterior angle is 45 degrees, then the number of sides is 360/45 = 8.\r
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\n" ); document.write( "\n" ); document.write( "Solution 2:
\n" ); document.write( "The sum of the measures of the interior angles of an n-gon is \"180%28n-2%29\". Divide this by n to get the average measure. Since each interior angle measures 135, we have\r
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\n" ); document.write( "\n" ); document.write( "\"135+=+180%28n-2%29%2Fn\", which can be solved to obtain \"n+=+8\".
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