Question 248172
The two angles are complementary. The sum of the measure of the first angle and 1/4 of the second angle is 75 degrees. Find the measures of the angles.
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When two angles are complimentary, that just means that they add up to 90 degrees
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Let x = an angle (the first angle)
Then
(90-x) = the other angle (second angle)
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When it says,"The sum of the measure of the first angle and 1/4 of the second angle is 75 degrees." we can write this
x + {{{1/4}}}(90-x) = 75
solve this for x and we have one of the angles
Multiply equation by 4 to get rid of the denominator, results
4x + (90-x) = 4(75)
4x - x + 90 = 300
3x = 300 - 90
3x = 210
x = {{{210/3}}}
x = 70 degrees is the first angle
then
90 - 70 = 20 degrees is the second angle
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Now, I will let you answer the following questions
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What is the measure of the smaller angle?
What is the measure of the other angle?
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Check solution in the statement
"The sum of the measure of the first angle and 1/4 of the second angle is 75 degrees."
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You are right!  Merry Christmas to you and your family also!   Carl