SOLUTION: The sum of the measures of 2 complementary angles exceeds the difference of the measures of their supplements by 32 degrees. Find the measure of each angle.

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Question 898544: The sum of the measures of 2 complementary angles exceeds the difference of the measures of their supplements by 32 degrees. Find the measure of each angle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y are the measures of two complementary angles.

x+y=90.

The rest of the description transcribes to 90-%28%28180-x%29-%28180-y%29%29=2.
You use meaning of supplementary angles, that their sum is 180 degrees.

Simplify the more complicated equation.
90-%28180-180-x%2By%29=2
90-%28y-x%29=2
90%2Bx-y=2
x-y=-88
y-x=88

NOW you have a simplifies SYSTEM of equations:
system%28x%2By=90%2Cy-x=88%29

If you begin with elimination method, you eliminate x and solve for y value.
x%2By%2By-x=90%2B88
2y=90%2B88
y=45%2B44
highlight%28y=89%29

This means highlight%28x=1%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the measures of 2 complementary angles exceeds the difference of the measures of their supplements by 32 degrees. Find the measure of each angle.


Smaller complementary angle:  highlight_green%28highlight_green%2816%5Eo%29%29

Larger complementary angle:   highlight_green%28highlight_green%2874%5Eo%29%29

You can do the check!! 



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