document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78899>Question 78899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Could someone help me on these problems please? Thank you!<BR>\n" );
document.write( "1. A convex 14-gon has six interior angles that each measure 164 degrees. If the remaining interior angles are congruent, what is the measure of each remaining angle?\r<BR>\n" );
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document.write( "2. Polygon OPQRSTUVWXYZ is a regular dodecagon. If line QR and XY intersect at point J, find measure angle QJK. \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 #56597 by </B><A HREF=/tutors/aboutme.mpl?userid=mathdoc314><B>mathdoc314(58)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathdoc314><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=56597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<BR>\n" );
document.write( "The exterior angles add up to 360 total.<BR>\n" );
document.write( "This is a convex 14-gon.<BR>\n" );
document.write( "If six of the interior angles each meausre 164 degrees and the remaining ones are congruent then:\r<BR>\n" );
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document.write( "8 x + 6 * (180-164) = 360<BR>\n" );
document.write( "8 x + 6 * 16 = 360<BR>\n" );
document.write( "8x + 96 = 360<BR>\n" );
document.write( "8x = 264<BR>\n" );
document.write( " x = 264 / 8 = 33 degrees<BR>\n" );
document.write( "The remaining interior angles measure (180-33) degrees which is 157\r<BR>\n" );
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document.write( "It is a miracle for sure\r<BR>\n" );
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document.write( "2. This is pretty funny.  The main problem is in counting the letters\r<BR>\n" );
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document.write( "QR to RS: 1<BR>\n" );
document.write( "RS to ST: 2<BR>\n" );
document.write( "ST to TU: 3<BR>\n" );
document.write( "TU to UV: 4<BR>\n" );
document.write( "UV to VW: 5<BR>\n" );
document.write( "VW to WX: 6<BR>\n" );
document.write( "WX to XY: 7<BR>\n" );
document.write( "There are only 12 sides on this thing so I have gone around more than halfway.  The right number to use for the number of angles turned is 5\r<BR>\n" );
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document.write( "The angles are all the same measure going from one side to another in going around this regular dodecahedron (12 sides) and they measure 360/12 degrees which is 30 degrees on each turn\r<BR>\n" );
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document.write( "The answer, I think, is 30 degrees * 5 turns which is 150 degrees<BR>\n" );
document.write( "You may want to draw a diagram to see if this is reasonable.\r<BR>\n" );
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