document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627564>Question 627564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i find the exterior angle of a convex polygon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394979 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=394979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two theorems that you can use to find the measure of interior angles of a convex polygon. One theorem works only for triangles. The other theorem works for all convex polygons, including triangles. \r<BR>\n" );
document.write( "\n" );
document.write( "Let's take a look at the theorem for triangles first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.  The sum of the interior angles  of a triangle is always <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "\n" );
document.write( "Since the polygons can be divided into triangles, and since each triangle has 180°, you just multiply the number of triangles by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >° to get the sum of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interior+ ALIGN=MIDDLE  ALT=\"interior+\"   DISABLED_style= \"max-width:90%; height:auto;\" >angles.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=180%28n-2%29 ALIGN=MIDDLE  ALT=\"s=180%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then divide it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (number of the sides of a polygon)  in order to calculate the measure of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=interior+ ALIGN=MIDDLE  ALT=\"interior+\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=180%28n-2%29%2Fn ALIGN=MIDDLE  ALT=\"s=180%28n-2%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use this theorem to find the measure of exterior angles of a convex polygon.\r<BR>\n" );
document.write( "\n" );
document.write( "2. The sum of the exterior angles  of a convex polygon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+always ALIGN=MIDDLE  ALT=\"+always\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember that a straight angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "\n" );
document.write( "The interior angle is always supplementary to an exterior angle at that vertex. They always add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, even for a concave polygon. \r<BR>\n" );
document.write( "\n" );
document.write( "Convex case:\r<BR>\n" );
document.write( "\n" );
document.write( "In the case of convex polygons, where all the vertices point \"outwards\" away form the interior, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=exterior+ ALIGN=MIDDLE  ALT=\"exterior+\"   DISABLED_style= \"max-width:90%; height:auto;\" >angles are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=always ALIGN=MIDDLE  ALT=\"always\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=outside ALIGN=MIDDLE  ALT=\"outside\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the polygon. \r<BR>\n" );
document.write( "\n" );
document.write( "Although there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+possible ALIGN=MIDDLE  ALT=\"+possible\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+exterior+ ALIGN=MIDDLE  ALT=\"+exterior+\"   DISABLED_style= \"max-width:90%; height:auto;\" >angles at each vertex , but we usually only consider one per vertex, selecting the ones that all go around in the same direction, clockwise in the figure.\r<BR>\n" );
document.write( "\n" );
document.write( "Taken one per vertex in this manner, the exterior angles<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+always ALIGN=MIDDLE  ALT=\"+always\"   DISABLED_style= \"max-width:90%; height:auto;\" > add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "This is true no matter how many sides the polygon has, and regardless of whether it is regular or irregular, convex or concave.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );