SOLUTION: Three angles in a triangle add up to 180 degrees. The largest angle is two degrees more than twice the second largest angle. The smallest angle is 18 degrees less than the second

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Question 1136556: Three angles in a triangle add up to 180 degrees. The largest angle is two degrees more than twice
the second largest angle. The smallest angle is 18 degrees less than the second largest angle. Find
the measure of all three angles.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Three angles in a triangle add up to 180 degrees.
alpha+%2Bbeta%2Bgamma=180..........eq.1

if the largest angle alpha is two degrees more than twice
the second largest angle beta, we have
alpha=2beta%2B2..........eq.2
if the smallest angle gamma is 18 degrees less than the second largest angle beta, we have
gamma=beta-18......eq.3
go back to eq.1
alpha+%2Bbeta%2Bgamma=180..........eq.1, substitute alpha and gamma
2beta%2B2+%2Bbeta%2Bbeta-18=180.......solve for beta
4beta-16=180
4beta=180%2B16
4beta=196
beta=196%2F4
beta=49

go to alpha=2beta%2B2..........eq.2
alpha=2%2A49%2B2
alpha=100


go to gamma=beta-18......eq.3
gamma=beta-18
gamma=49-18
gamma=31
the measure of all three angles: alpha=100°, beta=49°, gamma=31°


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Three angles in a triangle add up to 180 degrees. The largest angle is two degrees more than twice
the second largest angle. The smallest angle is 18 degrees less than the second largest angle. Find
the measure of all three angles.
Three angles in a triangle add up to 180 degrees <======= NOT NECESSARY, since in most cases, people who're familiar with geometry DO KNOW this FACT about a TRIANGLE

Let the middle angle be M

Then the largest angle measures: 2M + 2, and the smallest angle = M - 18

We then get: M + 2M + 2 + M - 18 = 180

M + 2M + M = 180 + 16

4M = 196