document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564681>Question 564681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many regular polygons have an interior angle that measures between 100 and 149 degrees? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365452 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=365452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the degrees in an n-gon is 180(n-2), so for a regular polygon, the interior angle measure will be 180(n-2)/n. Therefore, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 100 \le \frac{180(n-2)}{n} \le 149\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 100n \le 180n - 360 \le 149n\">\r<BR>\n" );
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document.write( "The \"first\" inequality yields <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 80n - 360 \ge 0 \Rightarrow 80n \ge 360 \Rightarrow n \ge 4.5\">.\r<BR>\n" );
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document.write( "The \"second\" inequality yields <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 31n \le 360 \Rightarrow n \le 11.61...\">\r<BR>\n" );
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document.write( "Therefore, n is between 4.5 and 11.61; the only integer values of n that satisfy are 5, 6, ..., 11, or seven values.\r<BR>\n" );
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