SOLUTION: The measure of the largest angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is 10 degrees less than the measure of the largest angle.

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Question 934370: The measure of the largest angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is 10 degrees less than the measure of the largest angle. I don't know if I set this up right, so I am looking for the right answer.
What I did:
X + 1/2X - 10 = 180
1.5X = 190
X = 126.6 repeating.
I don't think that's right.
Thank you.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


the largest angle of a triangle is alpha
the smallest angle is beta
the third angle is gamma
alpha+%2Bbeta%2Bgamma=180........eq.1
given:
The measure of the largest angle of a triangle is twice the measure of the smallest angle.
=> alpha=2beta.....eq.2
The measure of the third angle is 10 degrees less than the measure of the largest angle.
=>gamma=alpha-10.....eq.3...substitute 2beta for alpha
gamma=2beta-10
2beta%2Bbeta%2B2beta-10=180......eq.1...........solve for alpha
5beta=180%2B10
5beta=190.
beta=190%2F5
highlight%28beta=38%29
go to alpha=2beta.....eq.2 plug in 38 for beta
alpha=2%2A38
highlight%28alpha=76%29
and
gamma=alpha-10.....eq.3.
gamma=76-10
highlight%28gamma=66%29