document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205368>Question 205368</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1405802111/algebrahomeworkh>Longman Mathematics for IGCSE Book 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> There are two polygons. The larger one has three times as many sides as the smaller one, and its angle sum is four times bigger. How many sides has the smaller polygon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155066 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=155066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if a polygon has x sides, then each angle of this polygon is:<BR>\n" );
document.write( "180 - (360/x)<BR>\n" );
document.write( "the angle sum of this polygon <BR>\n" );
document.write( "= x * (180 - (360/x))<BR>\n" );
document.write( "= 180x - 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let:<BR>\n" );
document.write( "number of smaller polygon's side = a<BR>\n" );
document.write( "angle sum of smaller polygon = 180a - 360<BR>\n" );
document.write( "number of larger polygon's side = b<BR>\n" );
document.write( "angle sum of larger polygon = 180b - 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b = 3a<BR>\n" );
document.write( "180b - 360 = 4 * (180a - 360)<BR>\n" );
document.write( "180*(3a) - 360 = 720a - 1440<BR>\n" );
document.write( "540a - 360 = 720a - 1440<BR>\n" );
document.write( "1440 - 360 = 720a - 540a<BR>\n" );
document.write( "1080 = 180a<BR>\n" );
document.write( "a = 1080/180 = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, the smaller polygon has 6 sides </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );