SOLUTION: please help me on this problem The difference between two supplementary angles is 10. find the acute angle. i really don't know if this is right but, s-s=10 (180-x)

SOLUTION: please help me on this problem The difference between two supplementary angles is 10. find the acute angle. i really don't know if this is right but, s-s=10 (180-x) - (

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

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