SOLUTION: the difference between two complementary angles is 50 degrees. what is the measure of the larger angle?

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Question 161930: the difference between two complementary angles is 50 degrees. what is the measure of the larger angle?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Complementary angles ALWAYS add to 90 degrees. So this means that x%2By=90. Since "difference between two complementary angles is 50 degrees", this means that x-y=50


So we have the system of equations:
system%28x%2By=90%2Cx-y=50%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-y%29=%2890%29%2B%2850%29


%28x%2Bx%29%2B%28y-y%29=90%2B50 Group like terms.


2x%2B0y=140 Combine like terms. Notice how the y terms cancel out.


2x=140 Simplify.


x=%28140%29%2F%282%29 Divide both sides by 2 to isolate x.


x=70 Reduce. So the first angle is 70 degrees.


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x%2By=90 Now go back to the first equation.


70%2By=90 Plug in x=70.


70%2By=90 Multiply.


y=90-70 Subtract 70 from both sides.


y=20 Combine like terms on the right side. So the second angle is 20 degrees


So our answer is x=70 and y=20. So the larger angle is 70 degrees.