document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997507>Question 997507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the interior angle of a polygon is 4 times of its exterior angle,find the no. of sides and the sum of the i nterior angles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615556 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the interior angle = 4 times the exterior angle.<BR>\n" );
document.write( "the interior angle and the exterior angle are supplementary.<BR>\n" );
document.write( "the interior angle plus the exterior angle = 180 degrees.<BR>\n" );
document.write( "since the interior angle = 4 times the exterior angle, then you can replace the interior angle with the equivalent value of 4 times the exterior angle to get:<BR>\n" );
document.write( "4 times the exterior angle plus the exterior angle = 180 degrees.<BR>\n" );
document.write( "combine like terms to get 5 times the exterior angle = 180 degrees.<BR>\n" );
document.write( "divide both sides of this equation by 5 to get:<BR>\n" );
document.write( "the exterior angle = 180 / 5 = 36 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get interior angle = 4 * exterior angle = 4 * 36 = 144 degrees.<BR>\n" );
document.write( "144 + 36 = 180 degrees so they are supplementary as required.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the exterior angle of the regular polygon is equal to 360 / number of sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for number of sides to get number of sides = 360 / exterior angle = 360 / 36 = 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the interior angle of the regular polygon is equal to (180 * (n-2)) / n<BR>\n" );
document.write( "this formula becomes 144 = (180 * (n-2)) / n.<BR>\n" );
document.write( "you want to solve this equation for n.<BR>\n" );
document.write( "multiply both sides of this equaiton by n to get 144 * n = 180 * (n-2)<BR>\n" );
document.write( "simplify to get 144 * n = 180 * n - 360<BR>\n" );
document.write( "add 360 to both sides of this equation and subtract 144 * n from both sides of this equaiton to get 360 = 180 * n - 144 * n.<BR>\n" );
document.write( "simplify to get 360 = 36 * n<BR>\n" );
document.write( "divide both sides of this equation by 36 to get 360 / 36 = n<BR>\n" );
document.write( "solve for n to get n = 360 / 36 = 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get 10 sides to the regular polygon either way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "something else to note:<BR>\n" );
document.write( "the exterior angle is equal to the central angle.<BR>\n" );
document.write( "the number of sides is equal to 360 / the central angle or 360 / the exterior angle.<BR>\n" );
document.write( "either formula will do.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "finding the number of sides using the interior angle is messier than finding the number of sides using the exterior angle.<BR>\n" );
document.write( "if you are given the interior angle, just subtract that from 180 to get the exterior angle and then use the number of sides = 360 / exterior angle to find the number of sides.<BR>\n" );
document.write( "it's much easier.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of sides is equal to 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sum of the interior angles is equal to 10 * 144 = 1440 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can also be found using the sum of the interior angles of a regular polygon which is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sum of interior angles = (180 * (n-2)) = 180 * 8 = 1440.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );