Question 495775: the measure of on angle is 24 degrees greater then the measure of its complement.what are the measure of the angles?
Answer by kingme18(98)   (Show Source):
You can put this solution on YOUR website! Let's call the measure of the angle we're talking about "m", and let's call its complement "c".
The measure of our angle is 24 degrees greater than the measure of its complement. If we take that apart:
The measure of our angle (I defined that to be "m")
is (means =)
24 degrees greater than (more than; this is addition)
the measure of its complement (I defined that to be "c")
So really, we have 
We also know that an angle plus its complement is 90 by definition (so, for example, 10 and 80 are complements because they add to 90). So  .
But we know that  from above. That means that instead of saying m in our second equation, we can say 24+c. So instead of  , we have  . All I did was exchanged m and 24+c. Now, we solve:
The measure of the angle's complement is 33 degrees.
At the beginning, you told me that our angle is 24 degrees greater than its complement, so it's 24+33=57 degrees.
To check, our angle plus its complement should equal 90: 57 + 33 = 90. It works :) The two angles are 57 and 33 degrees.
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