document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42202>Question 42202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the sum of the interior angles of a regular polygon is four times \r<BR>\n" );
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document.write( "the sum of its exterior angles.\r<BR>\n" );
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document.write( "Find the number of sides of this regular polygon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27327 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let each interior angle of the regular polygon = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Eo ALIGN=MIDDLE  ALT=\"x%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then, each exterior angle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180-x%29%5Eo ALIGN=MIDDLE  ALT=\"%28180-x%29%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let the no. of sides = n.<BR>\n" );
document.write( "Then sum of all interior angles = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nx%5Eo ALIGN=MIDDLE  ALT=\"nx%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that of all exterior angles = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28180-x%29%5Eo ALIGN=MIDDLE  ALT=\"n%28180-x%29%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Given: sum of all interior angles = 4 x (sum of all exteriors)<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nx+=+4n%28180-x%29 ALIGN=MIDDLE  ALT=\"nx+=+4n%28180-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2A180+-+4x ALIGN=MIDDLE  ALT=\"x+=+4%2A180+-+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+720 ALIGN=MIDDLE  ALT=\"5x+=+720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+720%2F5 ALIGN=MIDDLE  ALT=\"x+=+720%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 144\r<BR>\n" );
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document.write( "Thus each interior angle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%5Eo ALIGN=MIDDLE  ALT=\"144%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and each exterior angle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180-144%29%5Eo+=+36%5Eo ALIGN=MIDDLE  ALT=\"%28180-144%29%5Eo+=+36%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We know that the sum of all the exterior angles of a regular polygon 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;\" >.\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A36=360 ALIGN=MIDDLE  ALT=\"n%2A36=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=360%2F36 ALIGN=MIDDLE  ALT=\"n=360%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or n = 10\r<BR>\n" );
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document.write( "So the reqd. no. of sides of the regular polygon is 10. </SPAN>\n" );
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