SOLUTION: Cant figure this out. Help Please! :) The measure of the second angle of a triangle is 50 degrees more than that of the first. The measure of the third angle is 10 degrees le

Algebra ->  Equations -> SOLUTION: Cant figure this out. Help Please! :) The measure of the second angle of a triangle is 50 degrees more than that of the first. The measure of the third angle is 10 degrees le      Log On


   

Question 185531: Cant figure this out. Help Please! :)
The measure of the second angle of a triangle is 50 degrees more than that of the first. The measure of the third angle is 10 degrees less than twice the first. Find the measures of the angles.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let "x" be the measure of the first angle

Since "The measure of the second angle of a triangle is 50 degrees more than that of the first.", this means that the second angle is x%2B50 (ie add 50 to the measure of the first angle). Also, because the "measure of the third angle is 10 degrees less than twice the first.", this tells us that 2x-10


Now remember, for EVERY triangle, the sum of their angles is 180 degrees. So this means that

Angle 1 + Angle 2 + Angle 3 = 180

which becomes

%28x%29%2B%28x%2B50%29%2B%282x-10%29=180



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%28x%29%2B%28x%2B50%29%2B%282x-10%29=180 Start with the given equation.


4x%2B40=180 Combine like terms.


4x=180-40 Subtract 40 from both sides.


4x=140 Combine like terms on the right side.


x=%28140%29%2F%284%29 Divide both sides by 4 to isolate x.


x=35 Reduce.


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Answer:

So the answer is x=35


So the first angle is x=35

the second angle is 35%2B50=85

and the third angle is 2%2835%29-10=70-10=60


In other words, the measures of the three angles are: 35, 85, and 60 degrees