SOLUTION: One angle of a triangle is 24∘ less than twice the sum of the second and third angles. Find the measure of the largest angle in the triangle.

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Question 709693: One angle of a triangle is 24∘ less than twice the sum of the second and third angles. Find the measure of the largest angle in the triangle.
Answer by tjansen(4) About Me  (Show Source):
You can put this solution on YOUR website!
Call the three angles a,b,and c
1) a=2(b+c)-24(degrees) Given
2) a+b+c=180(degrees) Sum of angles of a triangle=180(degrees)
3) (b+c)=180(degrees)-a Subtract a from both sides of 2)
4) a=2(180(degrees)-a)-24(degrees) Substitute value of (b+c) from 3) in 1)
5) a=360(degrees)-2a-24(degrees) Distribute 2 over parenthesis in 4)
6) 3a=360(degrees)-24(degrees) Add 2a to both sides of 5)
7) 3a=336(degrees) Combine terms in 6)
8) a=112(degrees) Divide 7) by 3
9) (b+c)=180(degrees)-112(degrees) Rearrange 2)
10) (b+c)=68(degrees) combine terms in 9)
Therefore a=112(degrees) is the largest angle.
Note that we don't know what angle b or c equals individually, but we don't need that information to solve for the largest angle.