SOLUTION: The measures of two angles in a triangle are in the ratio of 2:4. The measure of the larger angle is 24 degrees less than 3 times the smaller angle. What is the measure of the larg

Algebra ->  Human-and-algebraic-language -> SOLUTION: The measures of two angles in a triangle are in the ratio of 2:4. The measure of the larger angle is 24 degrees less than 3 times the smaller angle. What is the measure of the larg      Log On


   

Question 374318: The measures of two angles in a triangle are in the ratio of 2:4. The measure of the larger angle is 24 degrees less than 3 times the smaller angle. What is the measure of the larger angle?
Answer: I believe the larger angle is 48 degrees. But that was by guessing.
I tried to solve 2 equations L = 2*S and L = 3*S - 24
But this didn't work.
Thanks in advance.
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
48 degrees CANNOT be the largest angle because.
One of the angles MUST be greater than 60 degree. (3*60=180)
-----------------------------------------------------------
x+2x+(3x-24)=180
6x=180+24
6x=204
x=204/6
x=34 degrees is the smaller angle.
3*34=68 degrees is the middle angle.
3*34-24=102-24=78 degrees is the largest angle.
Proof:
34+68+78=180
180=180