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

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) (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) (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
RELATED QUESTIONS
The measures of two complementary angles are in a ratio of 7:5 Find the Measure of the... (answered by checkley71)
Find the measure of the angle. Two complementary angles have measures in the ratio... (answered by jim_thompson5910)
The measures of two complementary angles are in the ratio 2:3. What is the measure of the (answered by Theo)
The measures of two complementary angles are in the ratio 1:5.Find the measure of each... (answered by Theo,amoresroy)
The measure of two complementary angles are in ratio 1 to 3. What are the measures of... (answered by jim_thompson5910,addingup)
Three angles are complementary. The ratio of their measures is 2:3:5. Find the measure of (answered by ewatrrr)
Two complementary angles are in a ratio of 2 3. Find the measure of the larger angle (answered by checkley79,lynnlo)
two complementary angles are in the ratio 4:11. find the measure of the smaller... (answered by erica65404,stanbon)
Two complementary angles are in the ratio of 3:5, how do I find the measure of the... (answered by unlockmath)