document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73685>Question 73685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what do all the angles inside a heptagon add up to ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52741 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=52741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the interior angle<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=internal_angle_of_polygon.solver>internal angle of polygon</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><BR>\n" );
document.write( "  <A  rel=nofollow HREF=interior-angles-of-polygons.lesson> Interior angle of a Regular Polygon</A><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The interior angles of any <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Rectangles/Polygon.wikipedia>Polygon</A> always add up to a constant value, which depends only on the number of sides. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. The sum of the interior angles of a polygon is given by the formula<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sum=180%2A%28n-2%29 ALIGN=MIDDLE  ALT=\"Sum=180%2A%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  where n  is the number of sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For a regular polygon, the total described above is spread evenly among all the interior angles, since they all have the same values.Hence all interior angles will be equal.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Therefore,<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Each+Interior+Angle=%28%28180%2A%28n-2%29%29%2Fn%29 ALIGN=MIDDLE  ALT=\"Each+Interior+Angle=%28%28180%2A%28n-2%29%29%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Each+Interior+Angle=%28180%2A%287-2%29%29%2F7=128.571428571429 ALIGN=MIDDLE  ALT=\"Each+Interior+Angle=%28180%2A%287-2%29%29%2F7=128.571428571429\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Conversion of angles from <b><A  rel=nofollow HREF=Degree_%28angle%29.wikipedia>degrees</A></b> to <b><A  rel=nofollow HREF=Radian.wikipedia>radian</A></b>:<BR>\n" );
document.write( "  The relation between two units of angle measurement is :<BR>\n" );
document.write( "   <BR>\n" );
document.write( "  2*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > rad = 360 degrees<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The Interior angle in Radians,<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Each+Interior+Angle=%28%28%28180%2A%28n-2%29%29%2Fn%29%2A2%2Api%2F360%29 ALIGN=MIDDLE  ALT=\"Each+Interior+Angle=%28%28%28180%2A%28n-2%29%29%2Fn%29%2A2%2Api%2F360%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Each+Interior+Angle=%28%28180%2A%287-2%29%29%2F7%29%2A2%2Api%2F360=2.24399475 ALIGN=MIDDLE  ALT=\"Each+Interior+Angle=%28%28180%2A%287-2%29%29%2F7%29%2A2%2Api%2F360=2.24399475\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Hence, The interior angle of a Polygon is 128.571428571429 degrees and 2.24399475 radians.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For more on this topic, See the lessons on <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polygons/Geometry-Area-of-Regular-Polygons.lesson> Geometry Area of Regular Polygon</A> <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Some more is on <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polygons/Geometry-Special-Quadrilaterals.lesson>Geometry Special Quadrilaterals</A><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Multiply this by 7 to find the sum of the 7 angles<BR>\n" );
document.write( "7(128.57)=899.99 degrees<BR>\n" );
document.write( "or<BR>\n" );
document.write( "7(2.24)=15.68 radians </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );