document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463054>Question 463054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to find the measures of the consecutive angles of a quadrilateral in the ratio form of 5:7:11:13. How do you find the measure of each angle, draw a quadrilateral, and explain why two sides must be parallel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317331 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=317331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum of the angles of a quadrilateral = 360.\r<BR>\n" );
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document.write( "since your angles are in the ratio of 5:7:11:13, you can use the general formula of 5x + 7x + 11x + 13x = 360 to solve for x and, from that, to derive each angle.\r<BR>\n" );
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document.write( "you get 36x = 360 which gets you x = 10 degrees.\r<BR>\n" );
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document.write( "this makes your angles 50, 70, 110 and 130 respectively.\r<BR>\n" );
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document.write( "label your quadrilateral starting from the top left and working to the top right and then to the bottom right and then to the bottom left ABCD.\r<BR>\n" );
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document.write( "A is top left<BR>\n" );
document.write( "B is top right<BR>\n" );
document.write( "C is bottom right<BR>\n" );
document.write( "D is bottom left\r<BR>\n" );
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document.write( "Angle A is 50 degrees<BR>\n" );
document.write( "Angle B is 70 degrees<BR>\n" );
document.write( "Angle C is 110 degrees<BR>\n" );
document.write( "Angle D is 130 degrees.\r<BR>\n" );
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document.write( "Extend AB a little more to the right and stop at E.\r<BR>\n" );
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document.write( "You have angle ABC which is equal to 70 degrees.<BR>\n" );
document.write( "You have angle EBC which is the supplement of ABC which is equal to 110 degrees.\r<BR>\n" );
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document.write( "The sides that will be shown to be parallel are sides AB and CD.\r<BR>\n" );
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document.write( "The line BC is a transversal that intersects both AB and CD.\r<BR>\n" );
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document.write( "The 2 alternate interior angles of these intersections are angles EBC and angle BCD.\r<BR>\n" );
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document.write( "Both these angles are 110 degrees.\r<BR>\n" );
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document.write( "If the alternate interior angles of 2 lines cut by a transversal are equal, then the lines are parallel.  This is either a theorem or a postulate that you should be able to find in your geometry text.\r<BR>\n" );
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document.write( "You can also prove AB is parallel to CD by extending line CD further to the left to stop at F.\r<BR>\n" );
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document.write( "The angle ADC is 130 (previously called angle D).\r<BR>\n" );
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document.write( "The angle ADF is equal to 50 degrees (supplement of 130 degrees).\r<BR>\n" );
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document.write( "Angle BAD = 50 degrees and angle ADF = 50 degrees.\r<BR>\n" );
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document.write( "These are alternate interior angles and they are equal, therefore the lines AB and CD are parallel to each other.\r<BR>\n" );
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document.write( "A picture of the arrangement is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/problems/quadrilateral_1.jpg\" alt = \"***** file not found *****\"/ ><BR>\n" );
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