SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-fourth of the second angle is 82.5. What is the measure of the smaller angle? What is the measure

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Question 260594: Two angles are complementary. The sum of the measure of the first angle and one-fourth of the second angle is 82.5. What is the measure of the smaller angle? What is the measure of the other angle?
Answer by mananth(16946) About Me  (Show Source):
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Two angles are complementary. The sum of the measure of the first angle and one-fourth of the second angle is 82.5. What is the measure of the smaller angle? What is the measure of the other angle?
Two adjacent angles are said to be complimentary when the sum of measures of the angles are = 90deg.
Let one angle be x.
then the other angle will be 90-x
1/4 of the second angle is 1/4*(90-x)
Their sum is = 90
so x + 1/4*(90-x)=82.5 Take the LCM of the fractions
(4x+90-x)/4 = 82.5
4x+90-x= 4*82.5
3x-90= 330
3x= 330-90=240
x=80.
So the other angle is 10. ( since they are complimentary)
The angles are 80 and 10