document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179357>Question 1179357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many sides has a regular polygon whose interior angle is 22½<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808878 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Since an interior angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%261%2F2=22.5 ALIGN=MIDDLE  ALT=\"22%261%2F2=22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees, its adjacent exterior angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-22.5=+157.5 ALIGN=MIDDLE  ALT=\"180-22.5=+157.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees. \r<BR>\n" );
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document.write( "Exterior angles of any polygon always add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees. With the polygon being regular, we can just divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+ ALIGN=MIDDLE  ALT=\"360+\"   DISABLED_style= \"max-width:90%; height:auto;\" >by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=157.5 ALIGN=MIDDLE  ALT=\"157.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the number of sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   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=360%2F157.5=2.2857142857142856 ALIGN=MIDDLE  ALT=\"n=360%2F157.5=2.2857142857142856\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > a regular polygon whose interior angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%261%2F2 ALIGN=MIDDLE  ALT=\"22%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >° \r<BR>\n" );
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document.write( "double check this way:\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of sides of a regular polygon whose interior angles are each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.5 ALIGN=MIDDLE  ALT=\"22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >°.\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n-2%29%2Fn%29%2A180+=+22.5 ALIGN=MIDDLE  ALT=\"%28%28n-2%29%2Fn%29%2A180+=+22.5\"   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=%28n-2%29180=+22.5n ALIGN=MIDDLE  ALT=\"%28n-2%29180=+22.5n\"   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=180n-360=+22.5n ALIGN=MIDDLE  ALT=\"180n-360=+22.5n\"   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=180n-22.5n=+360 ALIGN=MIDDLE  ALT=\"180n-22.5n=+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=157.5n=+360 ALIGN=MIDDLE  ALT=\"157.5n=+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=n=+360%2F157.5 ALIGN=MIDDLE  ALT=\"n=+360%2F157.5\"   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=+2.2857142857142856 ALIGN=MIDDLE  ALT=\"n=+2.2857142857142856\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>\r<BR>\n" );
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document.write( "so, there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > a regular polygon whose interior angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%261%2F2 ALIGN=MIDDLE  ALT=\"22%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >° \r<BR>\n" );
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document.write( "Thus, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%261%2F2 ALIGN=MIDDLE  ALT=\"22%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >° cannot be an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interior ALIGN=MIDDLE  ALT=\"interior\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle of a regular polygon.\r<BR>\n" );
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