document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998399>Question 998399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the triangle, measure of angle 1 + the measure of angle 2+ the measure of angle three equals 180°. If the measure of angle three equals two times the measure of angle one and the measure of angle one equals the measure of angle 2 find the measure of angle three in degrees  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616177 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=616177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = measure of angle 1<BR>\n" );
document.write( "let b = measure of angle 2<BR>\n" );
document.write( "let c = measure of angle 3\r<BR>\n" );
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document.write( "measure of angle 3 equals 2 times the measure of angle 1.\r<BR>\n" );
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document.write( "equation for that is c = 2 * a\r<BR>\n" );
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document.write( "measure of angle 1 equals measure of angle 2.\r<BR>\n" );
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document.write( "equation for that is a = b\r<BR>\n" );
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document.write( "sum of the angles is 180 degrees.\r<BR>\n" );
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document.write( "equation for that is a + b + c = 180\r<BR>\n" );
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document.write( "you have 3 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "a + b + c = 180<BR>\n" );
document.write( "c = 2 * a<BR>\n" );
document.write( "a = b\r<BR>\n" );
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document.write( "subce a = b, let's replace b with a in the first equation to get:\r<BR>\n" );
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document.write( "a + a + c = 180\r<BR>\n" );
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document.write( "since c = 2 * a, let's replace x with 2 * a in the first equation to get:\r<BR>\n" );
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document.write( "a + a + 2 * a = 180\r<BR>\n" );
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document.write( "comtine like terms to get:\r<BR>\n" );
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document.write( "4 * a = 180\r<BR>\n" );
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document.write( "divide both sides of this equation by 4 to get:\r<BR>\n" );
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document.write( "a = 180 / 4 = 45 degrees.\r<BR>\n" );
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document.write( "since c is equal to 2 * a, then x must be equal to 90 degrees.\r<BR>\n" );
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document.write( "since a = b, then b must be equal to 45 degrees.\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "a = 45<BR>\n" );
document.write( "b = 45<BR>\n" );
document.write( "c = 90\r<BR>\n" );
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document.write( "the sum is 280 as it should be.\r<BR>\n" );
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document.write( "you are asked to find the measure of angle 3 in degrees.\r<BR>\n" );
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document.write( "since c = measure of angle 3, then angle 3 must be equal to 90 degrees.\r<BR>\n" );
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document.write( "these solutions satisfy all 3 equations.\r<BR>\n" );
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document.write( "a + b + c = 45 + 45 + 90 = 180 (good)<BR>\n" );
document.write( "c = 2 * a = 2 * 45 = 90 (good)<BR>\n" );
document.write( "a = b = 45 (good)\r<BR>\n" );
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document.write( "everything checks out - solution is good.\r<BR>\n" );
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document.write( "angle 3 is equal to 90 degrees.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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