SOLUTION: The measure of one angle is 24 degrees greater than the measure of its compliment.What are the measures of the angles?

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Question 648280: The measure of one angle is 24 degrees greater than the measure of its compliment.What are the measures of the angles?
Answer by MathLover1(20849) About Me  (Show Source):
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complementary angles are angles whose measures sum to 90°
let's angles be alpha and beta
so, alpha%2Bbeta=90.....1
given: the measure of one angle is 24 degrees greater than the measure of its compliment
so, alpha=beta%2B24........substitute it in equation 1
beta%2B24%2Bbeta=90.....solve for beta
2%2Abeta=90-24
2%2Abeta=66
highlight%28beta=33%29...now find alpha

alpha=90-beta
alpha=90-33
highlight%28alpha=57%29