SOLUTION: The first angle of a triangle is 10� less than the second angle. The third angle is three times the second angle. What is the measure of the second angle?

Question 467864: The first angle of a triangle is 10� less than the second angle. The third angle is three times the
second angle. What is the measure of the second angle?
Found 2 solutions by mananth, gwendolyn:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let second angle = x
First angle = x-10
Third angle = 3x
Sum of all angles = 180 deg
x+x-10+3x=180
5x-10=180
5x=190
x=38 deg==> second angle
Answer by gwendolyn(128) (Show Source): You can put this solution on YOUR website!
let f=the first angle
let s=the second angle
let t=the third angle
Remember that the angles in a triangle always add up to 180 degrees, so:
f+s+t=180
The first angle is equal to the second angle minus 10 degrees, so:
f=s-10
The third angle is equal to three times as much as the second angle, so:
t=3s
We can plug these equations into the first equation to get:
s-10+s+3s=180
Then, we can add 10 to both sides of the equation:
s+s+3s=190
Next, we combine like terms:
5s=190
Finally, we divide by 5:
s=38
We can plug this in to find other values.
t=3*38
t=114
f=38-10
f=28
So, the angles are 28, 38, and 144 degrees.
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