SOLUTION: if 2 angles are complementary , find the measure of the smallest angle of the measures of two angles are in the ratio of 3:1

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Question 823837: if 2 angles are complementary , find the measure of the smallest angle of the measures of two angles are in the ratio of 3:1
Found 2 solutions by 2897696, jim_thompson5910:
Answer by 2897696(96) About Me  (Show Source):
You can put this solution on YOUR website!
from the ratio 3:1 we can say its basically 3
since the 1 is representing the "small" portion of the complementary angle, we can make the variable x
Since 3 is representing the big portion of the complementary angle. because 3 is 3 times bigger than 1 we can make the big side equal to 3x
we know a complementary angle equals 90 degrees so we can make an equation using the variables that we made for the big angle and small angle.
x+3x=90
simplify equation
4x=90
x=22.5 <== this is the answer to the small angle
If you also want to find the big angle plug x into the big angle variable
3x-->3(22.5)=67.5 <=== this is the big angle amount



Answer:
small angle =22.5 (degrees)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The angles are in ratio 3:1 so if x is one angle, then 3x has to be the other. They are complementary, so they must also add to 90

3x + x = 90

4x = 90

x = 90/4

x = 22.5

3x = 3*22.5

3x = 67.5


Answer: Smallest angle is 22.5 degrees