document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090543>Question 1090543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the measure of an interior angle and an exterior angle of a regular decagon.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704985 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=704985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I find the exterior angles to be easier to figure out.<BR>\n" );
document.write( "An exterior angle is the change in direction at a vertex as you go around the polygon.<BR>\n" );
document.write( "The sum of all the exterior angles is <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( "a whole turn around the polygon, off course.<BR>\n" );
document.write( "For regular polygons, the angle is the same at each vertex.<BR>\n" );
document.write( "For a regular dodecagon, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertices, each exterior angle measures<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2F12=30%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo%2F12=30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , off course.<BR>\n" );
document.write( "Each interior angle is supplementary to an adjacent exterior angle,<BR>\n" );
document.write( "so in this case, each interior angle would measure<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo-30%5Eo=150%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo-30%5Eo=150%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Just in case your teacher wants to see formulas,<BR>\n" );
document.write( "the reasoning above would give you<BR>\n" );
document.write( "<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;\" > for the measure of the exterior angle of an n-hon (a polygon with n sides), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2A%28n-2%29%2Fn ALIGN=MIDDLE  ALT=\"180%2A%28n-2%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the measure of each interior angle.<BR>\n" );
document.write( "That last formula can also be thought as coming from the fact that all the interior angles add up to the angles of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-2%29 ALIGN=MIDDLE  ALT=\"%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangles you can make by connecting one vertex (choose any) to the other vertices with straight lines. </SPAN>\n" );
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