document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=14476>Question 14476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does anyone know how to do this?<BR>\n" );
document.write( "  Q.) Find the measure of each acute interior angle of a regular pentoGRAM.<BR>\n" );
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document.write( "I know that the triangles of a pentogram have two equal sides and and two congruent angles. And I know that if I divide the pentogram into triangles I get 8 triangles so the sum of the measures of the insides of the intire pentogram is 8x180 = 1440<BR>\n" );
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document.write( "all of the little trianles formed by the pentogram will be the same measure.<BR>\n" );
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document.write( "Maybe this can help, these are the theorems and corollaries being used in this section:\r<BR>\n" );
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document.write( "Theorem 2.5.2 : The sum(S)of the measures of the interior angles of a polygon with (n) sides is given by S=(n-S)*180 (note that n>2 for any polygon)<BR>\n" );
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document.write( "Theroem 2.5.1 : The total number of diagonals(D) in a polygone on (n) sides  is given by the formula:    D= (n)(n-3) divided by 2<BR>\n" );
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document.write( "Corollary 2.5.3 : The measure (I) of each interior angle of a regular polygon of (n) sides is:     I=(n-2)*180 degrees divided by (n)<BR>\n" );
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document.write( "Corollary 2.5.4 : The sum of four interior angles of a quadrilateral is 360 degrees.<BR>\n" );
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document.write( "Corollary 2.5.5 : The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360 degrees<BR>\n" );
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document.write( "Corollary 2.5.6 : The measure(E) of each exterior angle of a regular polygon  of (n) sides is      E= 360 degrees divided by (n)<BR>\n" );
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document.write( "I went to tutoring at the college for this problem and the tutor kept pulling numers out of the sky...none of what she said made sense and she never got the right answer. I am getting ready to give up. \r<BR>\n" );
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document.write( "she kept telling me that one angle was 72 degrees and the other two angles are 108 degrees each.<BR>\n" );
document.write( "But the sum of the measure of each of the triangles is supposed to equal 180 and that we are looking for an ACUTE angle and I told her and she didn't know what I was talking about. The answer is supposed to be 36 degrees\r<BR>\n" );
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document.write( "THANKS IN ADVANCE FOR YOUR HELP. =)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7248 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=7248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Wow! That's a ton of information for one small problem.\r<BR>\n" );
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document.write( "A regular pentagram (AKA Pentacle, but not Penotgram) is a five-pointed star formed by five straight lines connecting the vertices of a regular pentagon and enclosing another regular pentagon in the completed figure.<BR>\n" );
document.write( " The triangles of the pentagram thus formed are, as you point out, isosceles triangles, whose base angles, as you also point out, are congruent.\r<BR>\n" );
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document.write( "Now, if you know the measure of these congruent base-angles of the isosceles triangeles, then you can find the measure of the third angle.\r<BR>\n" );
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document.write( "Start with the regular pentagon on the inside of the figure.  The measure of each interior angle is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%285-2%29%28180%29%2F5 ALIGN=MIDDLE  ALT=\"A+=+%285-2%29%28180%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 108 degrees.\r<BR>\n" );
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document.write( "You will note that this angle is the supplement of a base angle of one of the triangles of the pentagram.<BR>\n" );
document.write( "Therefore, the base angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+-+108+=+72 ALIGN=MIDDLE  ALT=\"180+-+108+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.<BR>\n" );
document.write( "The other base angle is also 72 degrees (congruent angles).<BR>\n" );
document.write( "The third angle is then: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+-+2%2872%29%29+=+180+-+144 ALIGN=MIDDLE  ALT=\"180+-+2%2872%29%29+=+180+-+144\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 36 degrees.\r<BR>\n" );
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document.write( "You are asked to find the measure of each interior angle of the regular pentagram. This is the same as the third angle of the triangle which is 36 degrees.  </SPAN>\n" );
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