SOLUTION: If an angle is 60 less than twice it's complement find the ratio of the angle to its complement. If an angle is 30 more than twice it`s complement, find the ratio of the smaller

Algebra ->  Angles -> SOLUTION: If an angle is 60 less than twice it's complement find the ratio of the angle to its complement. If an angle is 30 more than twice it`s complement, find the ratio of the smaller      Log On


   

Question 547713: If an angle is 60 less than twice it's complement find the ratio of the angle to its complement.
If an angle is 30 more than twice it`s complement, find the ratio of the smaller to the larger angle.
Found 2 solutions by mananth, mathie123:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let angle be x
complement = 90-x
x=2(90-x)-60
x=180-2x-60
x=120-2x
3x=120
x=40
complement = 50
Ratio = 40/50 = 4/5
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Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
Let's recall what complementary angles really are:
Two angles are complement if they sum to 90 degrees.
Okay, so for the first question we will let x be the angle so the other angle must be x-60. Since they are each others complement we know:
%28x-60%29%2Bx=90
2x-60=90
2x-60%2B60=90%2B60
2x=150
2x%2F2=150%2F2
x=75
So the two angles are 75 and 75-60=15.
This means that the ratio between the two is 75:15 which can be reduced to 5:1.


For the second question, it is very similar...
Let y be the angle so then the other angle is y-30.
y%2B%28y-30%29=90
2y-30=90
2y=120
y=60
So the two angles are 60 and 60-30=30.
This means that the ratio of the smaller to the larger angle is 30:60 which can be reduced to 1:2.