document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669167>Question 669167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ratio of number of sides of 2 regular polygon is 5:6. & ratio of there each  interior angle is 24:25.find the number of sides of each polygon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416182 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=416182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your solution is that:<BR>\n" );
document.write( "n1 = 10<BR>\n" );
document.write( "n2 = 12<BR>\n" );
document.write( "a1 = 144<BR>\n" );
document.write( "a2 = 150\r<BR>\n" );
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document.write( "n = number of sides.<BR>\n" );
document.write( "a = measure of the interior angle.<BR>\n" );
document.write( "1 is for polygon number 1<BR>\n" );
document.write( "2 is for polygon number 2\r<BR>\n" );
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document.write( "there's a lot of arithmetic involved, but the basics of the solution is as follows:\r<BR>\n" );
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document.write( "you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n1%2Fn2+=+5%2F6 ALIGN=MIDDLE  ALT=\"n1%2Fn2+=+5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2Fa2+=+24%2F25 ALIGN=MIDDLE  ALT=\"a1%2Fa2+=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the formula for a1 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n1-2%29+%2A+180%29+%2F+n1 ALIGN=MIDDLE  ALT=\"%28%28n1-2%29+%2A+180%29+%2F+n1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the formula for a2 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n2-2%29+%2A+180%29+%2F+n2 ALIGN=MIDDLE  ALT=\"%28%28n2-2%29+%2A+180%29+%2F+n2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a1%2Fa2+=+24%2F25 ALIGN=MIDDLE  ALT=\"a1%2Fa2+=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can substitute for a1 and a2 in that ratio to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+%2F++%28%28%28n2-2%29+%2A+180%29+%2F+n2%29+=+24%2F25 ALIGN=MIDDLE  ALT=\"%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+%2F++%28%28%28n2-2%29+%2A+180%29+%2F+n2%29+=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can cross multiply to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2A+%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+=++24+%2A+%28%28%28n2-2%29+%2A+180%29+%2F+n2%29 ALIGN=MIDDLE  ALT=\"25+%2A+%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+=++24+%2A+%28%28%28n2-2%29+%2A+180%29+%2F+n2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you have 1 equation in 2 unknowns.<BR>\n" );
document.write( "you can reduce the number of unknowns by taking the ratio of n1 to n2 and solving for n2.\r<BR>\n" );
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document.write( "the ratio of n1 to n2 is given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n1%2Fn2+=+5%2F6 ALIGN=MIDDLE  ALT=\"n1%2Fn2+=+5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "from that, you can solve for n2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n2+=+6+%2A+n1+%2F+5 ALIGN=MIDDLE  ALT=\"n2+=+6+%2A+n1+%2F+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you now substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2A+n1+%2F+5 ALIGN=MIDDLE  ALT=\"6+%2A+n1+%2F+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for n2 in the equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2A+%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+=++24+%2A+%28%28%28n2-2%29+%2A+180%29+%2F+n2%29 ALIGN=MIDDLE  ALT=\"25+%2A+%28%28%28n1-2%29+%2A+180%29+%2F+n1%29+=++24+%2A+%28%28%28n2-2%29+%2A+180%29+%2F+n2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for n1.\r<BR>\n" );
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document.write( "once you find n1, you can then find n2 and you can then find a1 and a2.\r<BR>\n" );
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document.write( "the math is tricky but the process works and i was able to find n1 = 10 and n2 = 12.\r<BR>\n" );
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document.write( "from that i was able to get a1 = 144 and a2 = 150.\r<BR>\n" );
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document.write( "the ratios hold up so the solution is good.\r<BR>\n" );
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