River C is 100 miles longer than River D. If the sum of their lengths is 5,500 miles, what is the length of River D?
2 answers:
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Answer:
27°,63°
Step-by-step explanation:
Let the two angles be a and b.
They are complementary, meaning they add up to 90. Thus:
And we are told their difference is 36. Therefore:
Solve for the system of equations. Add b to both sides in the second equation:
Substitute this into the first:
Combine like terms;
Subtract 36:
Divide by 2:
So, b is 27 degrees.
Use the second equation again:
Now that we know b is 27, substitute:
Add 27 to both sides:
So, a is 63 degrees.
And we're done :)