document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139141>Question 1139141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the measure of a vertex angle, a central angle, and an exterior angle for a regular 40-gon figure\r<BR>\n" );
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document.write( "Asked other tutors and my teacher. still confusing me. any help appreciated. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756916 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a 40-gon figure is a figure that has 40 sides.\r<BR>\n" );
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document.write( "by the way, a 40-gon figure is called a Tetracontagon.\r<BR>\n" );
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document.write( "here's a link that has all the names of the gons, or at least a whole lot of them.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/List_of_polygons\" target = \"_blank\">https://en.wikipedia.org/wiki/List_of_polygons</a>\r<BR>\n" );
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document.write( "you have to scroll about halfway down the page to get to the gon names.\r<BR>\n" );
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document.write( "the sum of the interior angles of a polygon is equal to (n-2) * 180.\r<BR>\n" );
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document.write( "for example, the sum of the interior angles of a triangle is (3-2) * 180 = 180 and the sum of the interior angles of a quadrilateral is (4 - 2) * 180 = 360 and the sum of the interior angles of a pentagon is (5 - 2) * 180 = 540.\r<BR>\n" );
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document.write( "when we get to the tetracontagon, the sum of the interior angles would be (40 - 2) * 180 = 6840 degrees.\r<BR>\n" );
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document.write( "each interior angle of a regular tetracontagon would be 6840 / 40 = 171 degrees.\r<BR>\n" );
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document.write( "you can equate this procedure to finding the value of each interior angle of a regular quadrilateral = 360 / 4 = 90 degrees, or a regular triangle = 180 / 3 = 60 degrees.\r<BR>\n" );
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document.write( "a regular polygon is defined as a polygon that has all internal angles equal and all sides equal.\r<BR>\n" );
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document.write( "enough with internal angles.\r<BR>\n" );
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document.write( "each internal angles of a tetracontagon is equal to 171 degrees.\r<BR>\n" );
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document.write( "that would make each external angle of a tetracontagon equal to 180 - 171 = 9 degrees.\r<BR>\n" );
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document.write( "the other way to find the value of each external angle of a polygon is to divide 360 by the number of sides.\r<BR>\n" );
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document.write( "for a triangle, each external angle would be 360 / 3 = 120 degrees.<BR>\n" );
document.write( "this stands to reason because each internal angle is 60 degrees and each external angle is equal to 180 minus the value of each internal angle = 180 - 60 = 120.\r<BR>\n" );
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document.write( "with the tetracontagon, each external angle is therefore equal to 360 / 40 = 9 degrees.\r<BR>\n" );
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document.write( "i believe the central angle would be the same as the external angle.\r<BR>\n" );
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document.write( "that would make it equal to 9 degrees.\r<BR>\n" );
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document.write( "so, the general formulas for a regular polygon are:\r<BR>\n" );
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document.write( "sum of the interior angles is (n-2) * 180, where n is the number of sides.\r<BR>\n" );
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document.write( "each interior angle is (n-2) * 180 / n, where n is the number of sides.\r<BR>\n" );
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document.write( "each exterior angle is 360 / n, where n is the number of sides.\r<BR>\n" );
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document.write( "each central angle is 360 / n, where n is the number of sides (same formula as for each exterior angle).\r<BR>\n" );
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document.write( "the interior angle is also called the vertex angle.\r<BR>\n" );
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document.write( "there are numerous references to tetracontagons on the web.\r<BR>\n" );
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document.write( "here's a sample of a search page i did on google.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.google.com/search?q=tetracontagon&rlz=1C1CHBF_enUS839US839&oq=tetracontagon&aqs=chrome.0.69i59l2j69i60l3j0.1823j0j4&sourceid=chrome&ie=UTF-8\" target = \"_blank\">https://www.google.com/search?q=tetracontagon&rlz=1C1CHBF_enUS839US839&oq=tetracontagon&aqs=chrome.0.69i59l2j69i60l3j0.1823j0j4&sourceid=chrome&ie=UTF-8</a><BR>\n" );
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