document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003321>Question 1003321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest anglese </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620103 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28angles%29 ALIGN=MIDDLE  ALT=\"highlight%28angles%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "This phrase &nbsp;\"Angles of a pentagon in the ratio &nbsp;2:3:5:8:12.\"&nbsp; means that there is an angle &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;which is a &nbsp;\"<U>common measure</U>\" &nbsp;of the five angles in a way that\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;1-st angle is equal to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2alpha ALIGN=MIDDLE  ALT=\"2alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;2-nd angle is equal to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3alpha ALIGN=MIDDLE  ALT=\"3alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;3-rd angle is equal to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5alpha ALIGN=MIDDLE  ALT=\"5alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;4-th angle is equal to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8alpha ALIGN=MIDDLE  ALT=\"8alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;5-th angle is equal to &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12alpha ALIGN=MIDDLE  ALT=\"12alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then the sum of these angles is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+%2B+3+%2B+5+%2B+8+%2B+12%29%2Aalpha ALIGN=MIDDLE  ALT=\"%282+%2B+3+%2B+5+%2B+8+%2B+12%29%2Aalpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Aalpha ALIGN=MIDDLE  ALT=\"30%2Aalpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "From the other side, the sum of interior angles of a pentagon is (5-2)*180° = 3*180° = 540°.\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540%2F30 ALIGN=MIDDLE  ALT=\"540%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18°.\r<BR>\n" );
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document.write( "Now you can easily determine all 5 angles and determine the smallest and the largest. Do it yourself, please.\r<BR>\n" );
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