document.write( "Question 1083111: The number of sides in two regular polygons are as 5:4,and the difference between their angles is 9°;find the number of sides in the polygons. \n" ); document.write( "

Algebra.Com's Answer #697198 by ikleyn(52776) $\"\"$ $\"About$

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

\r\n" );
document.write( "Let n be the Greatest Common Divisor (GCD) of the numbers under the question.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then one polygon has 5n sides, while the other has 4n sides.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is well known fact that the sum of exterior angles of each (convex) polygon is 360 degs.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the exterior angle of the regular 5n-sided polygon is .\r\n" );
document.write( "\r\n" );
document.write( "Similarly, the exterior angle of the regular 4n-sided polygon is .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The difference between the corresponding exterior angles is 9 degs.\r\n" );
document.write( "\r\n" );
document.write( "It gives you an equation\r\n" );
document.write( "\r\n" );
document.write( " = 9,   or\r\n" );
document.write( "\r\n" );
document.write( " = 1,\r\n" );
document.write( "\r\n" );
document.write( " = 1,\r\n" );
document.write( "\r\n" );
document.write( " = 1,\r\n" );
document.write( "\r\n" );
document.write( "40 = 20n  --->  n =  = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the numbers of sides are 2*4 = 8 and 2*5 = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer. The regular polygons are octagon (8 sides) and decagon (10 sides).\r\n" );
document.write( "

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

\n" );