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) (Show Source): You can put this solution on YOUR website!
Complementary angles ALWAYS add to 90 degrees. So this means that . Since "difference between two complementary angles is 50 degrees", this means that
So we have the system of equations:
Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms. Notice how the y terms cancel out.
Simplify.
Divide both sides by to isolate .
Reduce. So the first angle is 70 degrees.
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Now go back to the first equation.
Plug in .
Multiply.
Subtract from both sides.
Combine like terms on the right side. So the second angle is 20 degrees
So our answer is and . So the larger angle is 70 degrees.
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