document.write( "Question 1135973: The measure of the exterior angles of a convex pentagon are consecutive integers. find the measure of each exterior angle. \n" ); document.write( "

Algebra.Com's Answer #753781 by ikleyn(52781) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "For any convex polygon, the sum of its exterior angles is equal to 360°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you need to find 5 consecutive integer numbers, whose sum is equal to 360.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can momentarily, immediately and instantly determine the middle of these 5 integer numbers: it is the number  = 72°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indeed, if n is this middle integer number, then the sequence itself is\r\n" );
document.write( "\r\n" );
document.write( "    (n-2), (n-1), n, (n+1) and ((n+2)\r\n" );
document.write( "\r\n" );
document.write( "with the sum  (n-2) + (n-1) + n + (n+1) + (n+2) = 5n,  which gives for the middle number n the expression and the value of  \r\n" );
document.write( "\r\n" );
document.write( "     n =  = 72.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the five angles are  70°, 71°, 72°, 73°  and  74°.     ANSWER\r\n" );
document.write( "

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

\n" );