document.write( "Question 478502: Interior angles of an octagon ABCDEFGH are in A.P.the largest and second an average of 153.find the average of least two. \n" ); document.write( "

Algebra.Com's Answer #327866 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!
Interior angles of an octagon ABCDEFGH are in A.P.the largest and second an average of 153.find the average of least two.
\n" ); document.write( "

\r
\n" );
document.write( "\n" );
document.write( "The nth term of an arithmetic sequence (numbers in A.P.) is
\n" );
document.write( "given by the formula:\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "The largest interior angle is the octagon is \r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "The second interior angle is the octagon is \r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "The average of the largest and second interior angles is\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "We are told this average is 153°\r
\n" );
document.write( "\n" );
document.write( "(eq. 1)  \r
\n" );
document.write( "\n" );
document.write( "The sum of n terms of an arithmetic sequence (numbers in A.P.) is
\n" );
document.write( "given by the formula:\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Substituting n=8\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "(eq. 2)   \r
\n" );
document.write( "\n" );
document.write( "The sum of the measurements of the interior angles of an n-sided
\n" );
document.write( "polygon is given by the epression \r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "For an octagon, n=8.\r
\n" );
document.write( "\n" );
document.write( "Sum of the interior angles of the octagon is \r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Therefore .  Substituting that in (eq. 2)\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Dividing both sides by 4\r
\n" );
document.write( "\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "or\r
\n" );
document.write( "\n" );
document.write( "{eq. 3)   \r
\n" );
document.write( "\n" );
document.write( "So we have this system consisting of eqs. 1 and 3\r
\n" );
document.write( "\n" );
document.write( " 
\n" );
document.write( " 
\n" );
document.write( "Solve the first equation of the system for \r
\n" );
document.write( "\n" );
document.write( "(eq. 4)   \r
\n" );
document.write( "\n" );
document.write( "Substituting in the second equation of the system\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Substituting in (eq. 4)\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "So the least interior angle of the octagon is the first
\n" );
document.write( "term 9°, and the common difference is d=36°\r
\n" );
document.write( "\n" );
document.write( "So the second term  = 9° + 36° = 45°.\r
\n" );
document.write( "\n" );
document.write( "The average of the least two interior angles is:\r
\n" );
document.write( "\n" );
document.write( "\r
\n" );
document.write( "\n" );
document.write( "Answer: 27°\r
\n" );
document.write( "\n" );
document.write( "Edwin \n" );
document.write( "

\n" );