document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694996>Question 694996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to find the measure of an interior angle and an exterior angle of a regular polygon with 16 sides </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428318 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=428318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As you go around a polygon, at each vertex, you change direction by a certain angle as you \"go around the corner\". That angle is an exterior angle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-5%2C5%2C-5%2C5%2C%0D%0Aarrow%281%2C-5%2C1%2C-2%29%2C+line%281%2C-2%2C1%2C0%29%2C%0D%0Aarrow%281%2C0%2C-2%2C3%29%2Cline%28-2%2C3%2C-4%2C5%29%2C%0D%0Agreen%28arrow%281%2C0%2C1%2C3%29%29%2Cgreen%28line%281%2C3%2C1%2C5%29%29%2C%0D%0Alocate%28-2.3%2C4%2Cexterior%29%2Clocate%28-1.2%2C3%2Cangle%29%2C%0D%0Alocate%28-3.5%2C1%2Cinterior%29%2Clocate%28-2%2C0%2Cangle%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you go all the way around a 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;\" > angles (and consequently <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), you have changed your direction by a whole turn around, a total of <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If it was a regular polygon, all those exterior angles were congruent (same measure), and the measure of each was <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Fn ALIGN=MIDDLE  ALT=\"2pi%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For a 16-sided regular polygon, the exterior angles measure<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2F16=highlight%2822.5%5Eo%29 ALIGN=MIDDLE  ALT=\"360%5Eo%2F16=highlight%2822.5%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F16=highlight%28pi%2F8%29 ALIGN=MIDDLE  ALT=\"2pi%2F16=highlight%28pi%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The interior angle is the \"corner\" you turned around. It is the supplement of the exterior angle. The measures of the interior and exterior angles add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In the case of your 16-sided regular polygon, the interior angles measure<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo-22.5%5Eo=highlight%28157.5%5Eo%29 ALIGN=MIDDLE  ALT=\"180%5Eo-22.5%5Eo=highlight%28157.5%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi-pi%2F8=highlight%287pi%2F8%29 ALIGN=MIDDLE  ALT=\"pi-pi%2F8=highlight%287pi%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "In general, the interior angle in a regular n-sided polygon measures<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo-360%5Eo%2Fn=n%2A180%5Eo%2Fn-2%2A180%5Eo%2Fn=%28n-2%29180%5Eo%2Fn ALIGN=MIDDLE  ALT=\"180%5Eo-360%5Eo%2Fn=n%2A180%5Eo%2Fn-2%2A180%5Eo%2Fn=%28n-2%29180%5Eo%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi-2pi%2Fn=n%2Api%2Fn-2pi%2Fn=%28n-2%29pi%2Fn ALIGN=MIDDLE  ALT=\"pi-2pi%2Fn=n%2Api%2Fn-2pi%2Fn=%28n-2%29pi%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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