document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947878>Question 947878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference between exterior angles of a \"n\" sided regular polygon and \"n+1\" sided regular polygon is 12 degrees. Find value of \"n\" \r<BR>\n" );
document.write( "\n" );
document.write( "Regards<BR>\n" );
document.write( "Vidhu </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578502 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the measures of the exterior angles of a convex polygon is always <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(The exterior angles are the angles of change of direction you must make at each corner (vertex) as you go around along the perimeter of the polygon, so of course<BR>\n" );
document.write( "a whole turn around the polygon will shift your direction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > to end in the same direction you started).<BR>\n" );
document.write( "In a regular polygon with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent exterior angles, all with the same measure: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2Fn ALIGN=MIDDLE  ALT=\"360%5Eo%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Similarly, the measure of each exterior angle of an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > sided polygon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2F%28n%2B1%29 ALIGN=MIDDLE  ALT=\"360%5Eo%2F%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2Fn ALIGN=MIDDLE  ALT=\"360%5Eo%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2Fn-360%5Eo%2F%28n%2B1%29 ALIGN=MIDDLE  ALT=\"360%5Eo%2Fn-360%5Eo%2F%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For this problem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5Eo=360%5Eo%2Fn-360%5Eo%2F%28n%2B1%29 ALIGN=MIDDLE  ALT=\"12%5Eo=360%5Eo%2Fn-360%5Eo%2F%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5Eo=360%5Eo%281%2Fn-1%2F%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"12%5Eo=360%5Eo%281%2Fn-1%2F%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5Eo ALIGN=MIDDLE  ALT=\"12%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=30%281%2Fn-1%2F%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"1=30%281%2Fn-1%2F%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=30%28%28n%2B1%29%2F%28n%28n%2B1%29%29-n%2F%28n%28n%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"1=30%28%28n%2B1%29%2F%28n%28n%2B1%29%29-n%2F%28n%28n%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=30%28%28n%2B1-n%29%2F%28n%28n%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"1=30%28%28n%2B1-n%29%2F%28n%28n%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=30%2F%28n%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"1=30%2F%28n%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29=30 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can say that the above equation is a quadratic equation,<BR>\n" );
document.write( "and we know that a quadratic equation can have at most two solutions.<BR>\n" );
document.write( "We could go through all kinds of algebra efforts to solve that equation,<BR>\n" );
document.write( "but we all know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A6=30 ALIGN=MIDDLE  ALT=\"5%2A6=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%2A%28-5%29=30 ALIGN=MIDDLE  ALT=\"%28-6%29%2A%28-5%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so we know that the two solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=5%29 ALIGN=MIDDLE  ALT=\"highlight%28n=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-6 ALIGN=MIDDLE  ALT=\"n=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(We also know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be an integer greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because a polygon must have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or more sides,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-6 ALIGN=MIDDLE  ALT=\"n=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes no sense). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );