document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=902233>Question 902233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value of each variable and the measure of each angle.<BR>\n" );
document.write( "give the equations used to find the measure.\r<BR>\n" );
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document.write( "there are two intersecting lines.<BR>\n" );
document.write( "the measure of the angle on the left is (4y) <BR>\n" );
document.write( "the measure of the angle on the top is (2x)<BR>\n" );
document.write( "the measure of the angle on the right is (x+y+10)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547173 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=547173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 intersecting lines form vertical angles and adjacent angles.\r<BR>\n" );
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document.write( "the angles opposite each other are the vertical angles.\r<BR>\n" );
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document.write( "the angles next to each other are the adjacent angles.\r<BR>\n" );
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document.write( "how can you tell the difference?\r<BR>\n" );
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document.write( "the angles that are on the opposite side of both lines are the vertical angles.\r<BR>\n" );
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document.write( "the angles that are on the opposite side of only one of the lines and on the same side of the other line are the adjacent angles.\r<BR>\n" );
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document.write( "your angles are:\r<BR>\n" );
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document.write( "one on the left is equal to 4y<BR>\n" );
document.write( "one on the right is equal to x + y + 10<BR>\n" );
document.write( "one on the top is equal to 2x\r<BR>\n" );
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document.write( "the one on the left and the one on the right are the vertical angles.<BR>\n" );
document.write( "they are on opposite sides of both lines.\r<BR>\n" );
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document.write( "the one on the top is a supplementary angle to the one on the left and also a supplementary angle to the one on the right.\r<BR>\n" );
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document.write( "that's because the angles are on the opposite side of only one of the lines while it is on the same side of the other line.\r<BR>\n" );
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document.write( "the equations formed are:\r<BR>\n" );
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document.write( "2x + 4y = 180 (adjacent therefore supplementary)<BR>\n" );
document.write( "2x + x + y + 10 = 180 (adjacent therefore supplementary)<BR>\n" );
document.write( "4y = x + y + 10 (vertical therefore equal)\r<BR>\n" );
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document.write( "we only need to solve two of these equations simultaneously to get the value of x and y that we need.\r<BR>\n" );
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document.write( "we'll choose 2x + 4y = 180 and 4y = x + y + 10.\r<BR>\n" );
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document.write( "2x + 4y = 180 doesn't need to be simplified.\r<BR>\n" );
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document.write( "4y = x + y + 10 needs to be simplified and converted to the same form as the first equation as follows:\r<BR>\n" );
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document.write( "subtract x and subtract y from both sides of the equation to get:\r<BR>\n" );
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document.write( "4y - x - y = 10\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3y - x = 10\r<BR>\n" );
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document.write( "rearrange the terms to get:\r<BR>\n" );
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document.write( "-x + 3y = 10\r<BR>\n" );
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document.write( "the two equations to solve simultaneously are:\r<BR>\n" );
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document.write( "2x + 4y = 180<BR>\n" );
document.write( "-x + 3y = 10\r<BR>\n" );
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document.write( "we'll multiply both sides of the second equation by 2 to get:\r<BR>\n" );
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document.write( "2x + 4y = 180<BR>\n" );
document.write( "-2x + 6y = 20\r<BR>\n" );
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document.write( "we'll add the two equations together to get:\r<BR>\n" );
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document.write( "10y = 200\r<BR>\n" );
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document.write( "we'll divide both sides of this equation by 10 to get:\r<BR>\n" );
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document.write( "y = 20\r<BR>\n" );
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document.write( "replace y with 20 in the first equation to get:\r<BR>\n" );
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document.write( "2x + 4y = 180 becomes:<BR>\n" );
document.write( "2x + 80 = 180<BR>\n" );
document.write( "subtract 80 from both sides of the equation to get:<BR>\n" );
document.write( "2x = 100<BR>\n" );
document.write( "divide both sides of the equation by 2 to get:<BR>\n" );
document.write( "x = 50\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "x = 50<BR>\n" );
document.write( "y = 20\r<BR>\n" );
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document.write( "let's see if they work.\r<BR>\n" );
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document.write( "the adjacent angles of 2x and 4y should add up to be equal to 180 degrees because they are supplementary7.\r<BR>\n" );
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document.write( "you get 2*50 + 4*20 = 100 + 80 = 180\r<BR>\n" );
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document.write( "since they add up to 180, the solution of x = 50 and y = 20 looks good so far.\r<BR>\n" );
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document.write( "the vertical angles of 4y and x+y+10 should be equal to each other.\r<BR>\n" );
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document.write( "you get 4*20 = 20 + 50 + 10 becomes 80 = 80.\r<BR>\n" );
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document.write( "this confirms the values of x and y are good in this equation as well.\r<BR>\n" );
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document.write( "you can go one step further since 2x + x + y + 10 are also supplementary and their sum should be equal to 180.\r<BR>\n" );
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document.write( "you get 2*50 + 50 + 20 + 10 = 100 + 80 = 180.\r<BR>\n" );
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document.write( "this confirms the values are good in this equation  as well.\r<BR>\n" );
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document.write( "looks like you're good all around, so your solution is:\r<BR>\n" );
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document.write( "x = 50<BR>\n" );
document.write( "y = 20<BR>\n" );
document.write( "the measure of the angle on the left is (4y) which is equal to 80 degrees.<BR>\n" );
document.write( "the measure of the angle on the top is (2x) which is equal to 100 degrees.<BR>\n" );
document.write( "the measure of the angle on the right is (x+y+10) which is equal to 80 degrees.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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