SOLUTION: Good day! I tried solving this problem. but, honestly, word problems in linear equations in one variable are quite confusing for me. I'm sorry for my weakness. i hope that you can

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Good day! I tried solving this problem. but, honestly, word problems in linear equations in one variable are quite confusing for me. I'm sorry for my weakness. i hope that you can       Log On


   

Question 173134: Good day! I tried solving this problem. but, honestly, word problems in linear equations in one variable are quite confusing for me. I'm sorry for my weakness. i hope that you can help me.
Problem: a) Given the non-right angles in a right triangle, if twice the first is 16 more than twice the second, find the angles.

thank you very much. God bless you.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a) Given the non-right angles in a right triangle, if twice the first is 16 more than twice the second, find the angles.
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The two non-right angesare complementary.
If one is x the other must be 90-x.
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EQUATION:
2(90-x) = 2x+16
180 - 2x = 2x + 16
4x = 164
x = 41 degrees (one of the angles)
90-x= 49 degrees (the other angle)
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
let x=first non-right angle and y=second non-right angle

The "non-right angles in a right triangle" are complementary. This means that they add to 90 degrees.


So this means that x%2By=90


Now since "twice the first is 16 more than twice the second", this tells us that 2x=2y%2B16


2x=2y%2B16 Start with the second equation


x=%282y%2B16%29%2F%282%29 Divide both sides by 2 to isolate x.


x=%282y%29%2F%282%29%2B%2816%29%2F%282%29 Break up the fraction


x=y%2B8 Reduce


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x%2By=90 Go back to the first equation


y%2B8%2By=90 Plug in x=y%2B8


2y%2B8=90 Combine like terms on the left side.


2y=90-8 Subtract 8 from both sides.


2y=82 Combine like terms on the right side.


y=%2882%29%2F%282%29 Divide both sides by 2 to isolate y.


y=41 Reduce. So the second angle is 41 degrees


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x=y%2B8 Go back to the previously isolated equation


x=41%2B8 Plug in y=41


x=49 Add. So the first angle is 49 degrees


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Answer:


So the solutions are x=49 and y=41 which means that the first non-right angle is 49 degrees and the second non-right angle is 41 degrees