document.write( "Question 1026768: The ratio of the interior angles of a pentagon is 4:4:5:5:6, find the largest interior and exterior angles. \n" ); document.write( "

Algebra.Com's Answer #642075 by ikleyn(52791) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The ratio of the interior angles of a pentagon is 4:4:5:5:6, find the largest interior and exterior angles.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let A, B, C, D and E be the interior angles of the given pentagon, in the corresponding ordering.\r\n" );
document.write( "The condition means that there is an angle which is the common measure of the given angles.\r\n" );
document.write( "Let x be the measure of this angle.\r\n" );
document.write( "\r\n" );
document.write( "Then A = 4x, B = 4x, C = 5x, D = 5x, E = 6x.\r\n" );
document.write( "\r\n" );
document.write( "The sum of interior angles of the pentagon is (5-2)*180° = 3*180° = 540°.\r\n" );
document.write( "\r\n" );
document.write( "It gives an equation\r\n" );
document.write( "\r\n" );
document.write( "4x + 4x + 5x + 5x + 6x = 540°,   or\r\n" );
document.write( "\r\n" );
document.write( "24x = 540°.\r\n" );
document.write( "\r\n" );
document.write( "Then x =  = 22.5°.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the interior angles are \r\n" );
document.write( "\r\n" );
document.write( "A = 4*22.5° = 90°,  B = 90°,  C = 112.5°,  D = 112.5°,  E = 135°.\r\n" );
document.write( "\r\n" );
document.write( "The largest interior angle is C = 135°.\r\n" );
document.write( "The largest exterior is 90°.\r\n" );
document.write( "

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

\n" );