document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983960>Question 983960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> - find the number of sides in a polygon whose interior angles are in arithmetical progression. the smallest being 120° and the common difference 5 °     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604889 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52813)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The sum of the interior angles of a given polygon is the sum of arithmetic progression with the first term &nbsp;120°&nbsp; and the common difference of &nbsp;5°, &nbsp;according to the condition. \r<BR>\n" );
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document.write( "So, &nbsp;it is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28120+%2B+%28%28n-1%29%2A5%29%2F2%29%2An ALIGN=MIDDLE  ALT=\"%28120+%2B+%28%28n-1%29%2A5%29%2F2%29%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees. \r<BR>\n" );
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document.write( "From the other side, &nbsp;it is &nbsp;180°*(n-2), &nbsp;according to the formula of sum of interior angles of a polygon.\r<BR>\n" );
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document.write( "Thus you have an equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28120+%2B+%28%28n-1%29%2A5%29%2F2%29%2An ALIGN=MIDDLE  ALT=\"%28120+%2B+%28%28n-1%29%2A5%29%2F2%29%2An\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2A%28n-2%29 ALIGN=MIDDLE  ALT=\"180%2A%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Simplify and solve it step by step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120n+%2B%28n%2A%28n-1%29%2A5%29%2F2 ALIGN=MIDDLE  ALT=\"120n+%2B%28n%2A%28n-1%29%2A5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2An+-+360 ALIGN=MIDDLE  ALT=\"180%2An+-+360\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240n+%2B+5n%28n-1%29 ALIGN=MIDDLE  ALT=\"240n+%2B+5n%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360n+-+720 ALIGN=MIDDLE  ALT=\"360n+-+720\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2+-+5n+-+120n+%2B720 ALIGN=MIDDLE  ALT=\"5n%5E2+-+5n+-+120n+%2B720\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2+-+125n+%2B+720 ALIGN=MIDDLE  ALT=\"5n%5E2+-+125n+%2B+720\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+25n+%2B+144 ALIGN=MIDDLE  ALT=\"n%5E2+-+25n+%2B+144\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This quadratic equation has two roots: &nbsp;n = 9&nbsp; and &nbsp;n = 16&nbsp; (use the quadratic formula or the Vieta's theorem). \r<BR>\n" );
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document.write( "So, &nbsp;the problem has two solutions: &nbsp;n = 9&nbsp; and &nbsp;n = 16.\r<BR>\n" );
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