SOLUTION: Can someone help me with angles? 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 ang

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Question 248172: Can someone help me with angles? 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.
What is the measure of the smaller angle?
What is the measure of the other angle?
Can someone please explain this to me? any help is appreciated, Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
:
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%2F4(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%2F3
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
:
What is the measure of the smaller angle?
What is the measure of the other angle?
:
:
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