document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191300>Question 1191300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the drawing in which <BR>\n" );
document.write( "AC intersects DB<BR>\n" );
document.write( " at point O to answer the question.\r<BR>\n" );
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document.write( "Two lines intersect at point O to form four angles.<BR>\n" );
document.write( "Line A C goes from point A in the top left, through point O in the center, to point C in the bottom right.<BR>\n" );
document.write( "Line D B goes from point D in the bottom left, through O on line A C, to point B in the top right.<BR>\n" );
document.write( "The angle at the bottom, ∠C O D, is labeled 1.<BR>\n" );
document.write( "The angle on the left, ∠D O A, is labeled 2.<BR>\n" );
document.write( "The angle at the top, ∠A O B, is labeled 3.<BR>\n" );
document.write( "The angle on the right, ∠B O C, is labeled 4.<BR>\n" );
document.write( "If <BR>\n" );
document.write( "m∠2 = \r<BR>\n" );
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document.write( "x<BR>\n" );
document.write( "2<BR>\n" );
document.write( " − 30<BR>\n" );
document.write( "	°<BR>\n" );
document.write( " <BR>\n" );
document.write( " and <BR>\n" );
document.write( "m∠3 = \r<BR>\n" );
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document.write( "x<BR>\n" );
document.write( "3<BR>\n" );
document.write( " + 60<BR>\n" );
document.write( "	°<BR>\n" );
document.write( " <BR>\n" );
document.write( ",<BR>\n" );
document.write( " find x and m∠2 in degrees.<BR>\n" );
document.write( "x	=	<BR>\n" );
document.write( "m∠2	=	<BR>\n" );
document.write( " °<BR>\n" );
document.write( "Need Help? Read It </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849120 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve for x and m∠2:\r<BR>\n" );
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document.write( "1. **Recognize the relationship between the angles:** ∠2 and ∠3 are vertical angles. Vertical angles are congruent, meaning they have the same measure.\r<BR>\n" );
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document.write( "2. **Set up an equation:** Since m∠2 = m∠3, we can write:\r<BR>\n" );
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document.write( "   x² - 30 = x³ + 60\r<BR>\n" );
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document.write( "3. **Rearrange the equation:** To solve for x, we need to rearrange the equation. However, this equation involves x² and x³, which makes it a cubic equation, and isn't easy to solve directly. The problem likely intended a linear relationship. It is possible there was a typo in the original problem. If we assume that the intended relationship was linear rather than polynomial, and assuming that the intended measures were m∠2 = x - 30 and m∠3 = x + 60, then we can proceed as follows:\r<BR>\n" );
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document.write( "   x - 30 = x + 60\r<BR>\n" );
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document.write( "4. **Solve for x:**<BR>\n" );
document.write( "   Subtract x from both sides:<BR>\n" );
document.write( "   -30 = 60  This is not possible.\r<BR>\n" );
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document.write( "   It's possible that there was a typo in the original problem.  If the angle measures were instead m∠2 = x - 30 and m∠3 = 2x + 60, then we would proceed as follows:\r<BR>\n" );
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document.write( "   x - 30 = 2x + 60<BR>\n" );
document.write( "   -90 = x\r<BR>\n" );
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document.write( "5. **Substitute x back into the equation for m∠2:**\r<BR>\n" );
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document.write( "   m∠2 = x - 30<BR>\n" );
document.write( "   m∠2 = -90 - 30<BR>\n" );
document.write( "   m∠2 = -120°\r<BR>\n" );
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document.write( "Since angle measures can't be negative, it's likely there was a typo in the original problem.  Double-check the given angle measures.  If they were m∠2 = x-30 and m∠3 = x+60, then there is no solution. If they were m∠2 = x-30 and m∠3 = 2x+60, then x = -90 and m∠2 = -120. \r<BR>\n" );
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document.write( "**If you can provide the correct angle measures, I can help you solve the problem accurately.**<BR>\n" );
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