document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175920>Question 1175920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the measure of one interior angle of a regular nonagon. Round to the nearest tenth, if necessary.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801686 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=801686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a nonagon is a 9 sided polygon.\r<BR>\n" );
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document.write( "if it's regular, then all sides are the same measure and all angles are the same measure.\r<BR>\n" );
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document.write( "you can find the measure of one internal angle in two distinct ways.\r<BR>\n" );
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document.write( "first way is to find the measure of each external angle.\r<BR>\n" );
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document.write( "the external angle of a polygon is the supplement of its corresponding internal angle.\r<BR>\n" );
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document.write( "the sum of the external angles of a polygon is always equal to 360 degrees.\r<BR>\n" );
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document.write( "if the polygon is a regular polygon, then the measure of each external angle is 360 / the number of sides of the polygon.\r<BR>\n" );
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document.write( "360 / 9 = 40 degrees.\r<BR>\n" );
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document.write( "the supplement of 40 degrees is 180 - 40 = 140 degrees.\r<BR>\n" );
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document.write( "that's the measure of each internal angle of the regular nonagon.<BR>\n" );
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document.write( "the other way is to use the formula for the sum of the internal angles of a polygon.\r<BR>\n" );
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document.write( "that formula is that the sum of the internal angles of a polygon is equal to 180 * (n-2), where n is the number of sides of the polygon.\r<BR>\n" );
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document.write( "using that formula, you get the sum = 7 * 180 = 1260 degrees.\r<BR>\n" );
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document.write( "divide that by 9 to get each internal angle of a regular nonagon = 1260 / 9 = 140 degrees.\r<BR>\n" );
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document.write( "you get the same answer either way.\r<BR>\n" );
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