document.write( "Question 1122231: The four angles of a quadrilateral form an arithmetic sequence. The largest is 15 degrees less than twice the smallest. What is the degree measure of the largest angle? \n" ); document.write( "

Algebra.Com's Answer #738295 by ikleyn(53646) $\"\"$ $\"About$

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

\r\n" );
document.write( "Let the smallest angle is x degrees and the largest is y degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The sum of all four interior angles of a quadrilateral is 360 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since four angles form arithmetic progression, the formula for their sum is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 360,   which implies\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x + y = 180.      (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The second equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     y = 2x + 15.     (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute eq(2) into eq(1). You will   get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     x + (2x+15) = 180,\r\n" );
document.write( "\r\n" );
document.write( "     3x = 180 - 15 = 165  ====>  x =  = 55.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The smallest angle is 55 degrees.   The greatest angle is  2x + 15 = 2*55 + 15 = 110 + 15 = 125 degrees.\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" );