document.write( "Question 1132141: The interior angle of a regular polygon is more by 144degree than its exterior angle.find the number of sides of regular polygon. \n" ); document.write( "

Algebra.Com's Answer #749059 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "The interior angle of a regular polygon is more by 144 degree than its exterior angle. Find the number of sides of regular polygon.
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document.write( "You are given\r\n" );
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document.write( "Int + Ext = 180      (1)\r\n" );
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document.write( "Int - Ext = 144      (2)     (\"The interior angle of a regular polygon is more by 144degree than its exterior angle.\")\r\n" );
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document.write( "Subtract equations (2) from equation (1) to get\r\n" );
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document.write( "    2*Ext = 180 - 144 = 36  degrees  ====>  Ext =  = 18 degrees.\r\n" );
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document.write( "Now use the fact that the sum of all exterior angles of a polygon is  equal to 360 degrees:\r\n" );
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document.write( "    n*Ext = 360,    which implies   n =  = 20.\r\n" );
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document.write( "ANSWER.  The number of sides of the given regular polygon is 20.\r\n" );
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