Question 185531
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+50}}} (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


{{{(x)+(x+50)+(2x-10)=180}}}




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{{{(x)+(x+50)+(2x-10)=180}}} Start with the given equation.



{{{4x+40=180}}} Combine like terms.



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



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



{{{x=(140)/(4)}}} 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+50=85}}}


and the third angle is {{{2(35)-10=70-10=60}}}



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