SOLUTION: Complementary angles are two angles whose measures add to 90 degrees. The ratio of the measures of two complementary angles is 4:11. What are the measures of the angles?

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Question 106102: Complementary angles are two angles whose measures add to 90 degrees. The ratio of the measures of two complementary angles is 4:11. What are the measures of the angles?
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the angles A and B.
1. A%2BB=90
2. A%2FB=4%2F11
Use equation 2 to solve for A in terms of B and substitute back into equation 1.
2. A%2FB=4%2F11
A=B%2A%284%2F11%29
Now into equation 1.
1. A%2BB=90
B%2A%284%2F11%29%2BB=90
B%2A%284%2F11%29%2BB%2A%2811%2F11%29=90
B%2A%2815%2F11%29=90
B=90%2A%2811%2F15%29
B=66
A=B%2A%284%2F11%29=66%2A%284%2F11%29=24
Check your answers.
1. A%2BB=90
24%2B66=90
90=90
Good answer.
2. A%2FB=4%2F11
24%2F66=4%2F11
%286%2F6%29%2A%284%2F11%29=4%2F11
4%2F11=4%2F11
Good answer.
Your angles are 24%5Eo and 66%5Eo