document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163744>Question 163744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This proof cannot be solved in the traditional two-column proof fashion. It has to be solved in an algebraic manner starting with an equation. Prove this theorem: One exterior angle for a regular polygon is 360/n, where n is the number of sides. Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120620 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=measure of exterior angle and y = measure of interior angle\r<BR>\n" );
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document.write( "We know that the formula for the interior angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interior_angle=180%28n-2%29%2Fn ALIGN=MIDDLE  ALT=\"interior_angle=180%28n-2%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=180%28n-2%29%2Fn ALIGN=MIDDLE  ALT=\"y=180%28n-2%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Also, remember that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=180 ALIGN=MIDDLE  ALT=\"x%2By=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > since the sum of the interior and exterior angle is 180\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=180-x ALIGN=MIDDLE  ALT=\"y=180-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Solve for \"y\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%28n-2%29%2Fn=180-x ALIGN=MIDDLE  ALT=\"180%28n-2%29%2Fn=180-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=180%28n-2%29%2Fn ALIGN=MIDDLE  ALT=\"y=180%28n-2%29%2Fn\"   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=180%28n-2%29=180n-xn ALIGN=MIDDLE  ALT=\"180%28n-2%29=180n-xn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by \"n\" to clear the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180n-360=180n-xn ALIGN=MIDDLE  ALT=\"180n-360=180n-xn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-360=-xn ALIGN=MIDDLE  ALT=\"-360=-xn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 180n from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-360%2F%28-n%29=x ALIGN=MIDDLE  ALT=\"-360%2F%28-n%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -n  to isolate x (which is the exterior angle)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=360%2Fn ALIGN=MIDDLE  ALT=\"x=360%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So this shows that for any regular n-gon, the exterior angle will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Fn ALIGN=MIDDLE  ALT=\"360%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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