document.write( "Question 557341: please help me on this problem\r
\n" ); document.write( "\n" ); document.write( "The difference between two supplementary angles is 10. find the acute angle.\r
\n" ); document.write( "\n" ); document.write( "i really don't know if this is right but,\r
\n" ); document.write( "\n" ); document.write( "s-s=10\r
\n" ); document.write( "\n" ); document.write( "(180-x) - (180-x) =10\r
\n" ); document.write( "\n" ); document.write( "have no idea if the equation is right, but i know the awnser is supposed to be 85 \n" ); document.write( "
Algebra.Com's Answer #362589 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the difference between supplementary angles is equal to 10.
\n" ); document.write( "let x = the angle.
\n" ); document.write( "let y = the supplementary angle.
\n" ); document.write( "your formula would be:
\n" ); document.write( "x + y = 180
\n" ); document.write( "assuming that x is the larger of the 2, your other equation would be:
\n" ); document.write( "x - y = 10
\n" ); document.write( "thee are 2 equations that need to be solved simultaneously.
\n" ); document.write( "add the 2 equations together to get:
\n" ); document.write( "2x = 190
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "x = 95
\n" ); document.write( "since x + y = 180, this means that:
\n" ); document.write( "y = 85 because:
\n" ); document.write( "95 + 85 = 180 and the angles are supplementary.
\n" ); document.write( "their difference is 10.
\n" ); document.write( "looks like your answer is that the angles are 95 degrees and 85 degrees.
\n" ); document.write( "you were asked for the acute angle.
\n" ); document.write( "that angle is 85 degrees.
\n" ); document.write( "fyi:
\n" ); document.write( "when you add 2 equations together, you are adding like terms together.
\n" ); document.write( "our 2 equations were:
\n" ); document.write( "x + y = 180
\n" ); document.write( "x - y = 10
\n" ); document.write( "when we added these equations together:
\n" ); document.write( "the x was added to the x to make 2x.
\n" ); document.write( "the y was added to the -y to make 0 (the y canceled out).
\n" ); document.write( "the 180 was added to the 10 to make 190.
\n" ); document.write( "that's how we resulted in:
\n" ); document.write( "2x = 190
\n" ); document.write( "this is called the elimination method for solving equations simultaneously, in case you are not familiar with it.
\n" ); document.write( "we could also have solved these equations simultaneously through substitution.
\n" ); document.write( "using that method, we would have done the following:
\n" ); document.write( "the equations are:
\n" ); document.write( "x + y = 180
\n" ); document.write( "x - y = 10
\n" ); document.write( "in this case, we would use the second equation to solve for x in terms of y.
\n" ); document.write( "we would get:
\n" ); document.write( "x = y + 10
\n" ); document.write( "we would then substitute that value of x for x in the first equation to get:
\n" ); document.write( "x + y = 180 becomes:
\n" ); document.write( "y + 10 + y = 180
\n" ); document.write( "we would combine like terms to get:
\n" ); document.write( "2y + 10 = 180
\n" ); document.write( "we would subtract 10 from both sides of the equation and then we would divide both sides of the equation by 2 to get:
\n" ); document.write( "y = 85
\n" ); document.write( "we would then go back to the first equation and substitute for y to get:
\n" ); document.write( "x + y = 180 becomes:
\n" ); document.write( "x + 85 = 180
\n" ); document.write( "subtract 85 from both sides of the equation to get:
\n" ); document.write( "x = 180 - 85
\n" ); document.write( "simplify to get:
\n" ); document.write( "x = 95.
\n" ); document.write( "we get the same answer through the method of substitution as we get through the method of elimination as we should.\r
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