document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464025>Question 464025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> each interior angle of each regular polygon is twice the measurement of each exterior angle.how many diagonals does the polygon have?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317897 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let be x degree the measure of an exterior angle, then the measure of an interior \r<BR>\n" );
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document.write( "angle is 2x degree. Assume that the regular polygon has n sides (or angles).\r<BR>\n" );
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document.write( "We know that the sum of the interior angles is :<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A2x=%28n-2%29%2A180 ALIGN=MIDDLE  ALT=\"n%2A2x=%28n-2%29%2A180\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the sum\r<BR>\n" );
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document.write( "of exterior angles is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Ax=360 ALIGN=MIDDLE  ALT=\"n%2Ax=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=360%2Fn ALIGN=MIDDLE  ALT=\"x=360%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substituting this value \r<BR>\n" );
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document.write( "for x in the first equation we get:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A2%2A360%2Fn=%28n-2%29%2A180 ALIGN=MIDDLE  ALT=\"n%2A2%2A360%2Fn=%28n-2%29%2A180\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A180=%28n-2%29%2A180 ALIGN=MIDDLE  ALT=\"4%2A180=%28n-2%29%2A180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=n-2 ALIGN=MIDDLE  ALT=\"4=n-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the number of angles is \r<BR>\n" );
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document.write( "six, our regular polygon is a hexagon, and the number of diagonals drawn from one \r<BR>\n" );
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document.write( "vertex is three less then the number of sides, 6-3=3 diagonals. </SPAN>\n" );
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