document.write( "Question 1118128: The ratio of the interior angle to the exterior angle of a regular polygon is 5 : 2. Find the number of sides of the polygon. \n" ); document.write( "

Algebra.Com's Answer #733382 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "According to the condition, the interior angle is 5x, while the exterior angle is 2x,\r\n" );
document.write( "\r\n" );
document.write( "where x is (an unknown) common measure of the two angles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since interior and exterior angles are supplementary, you have\r\n" );
document.write( "\r\n" );
document.write( "2x + 5x = 180 degrees,  or  7x = 180 degrees,  i.e.  x = .    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, the sum of exterior angles is 360 degrees:\r\n" );
document.write( "\r\n" );
document.write( "n*(2x) = 360 degrees,  or  n = .    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute here x =  from (2). You will get\r\n" );
document.write( "\r\n" );
document.write( "n =  =  = 7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The number of sides of the polygon is 7.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );