SOLUTION: In triangle ABC, angle A is twice the sum of angles B and C. Angle B is 24 degrees. What is the measure of Angle A? The answer is Angle A is 120 degrees but we can't figure ou

Algebra ->  Triangles -> SOLUTION: In triangle ABC, angle A is twice the sum of angles B and C. Angle B is 24 degrees. What is the measure of Angle A? The answer is Angle A is 120 degrees but we can't figure ou      Log On


   

Question 875750: In triangle ABC, angle A is twice the sum of angles B and C. Angle B is 24 degrees. What is the measure of Angle A?
The answer is Angle A is 120 degrees but we can't figure out how to get there. Help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"angle A is twice the sum of angles B and C" so A = 2*(B+C)


Since B = 24, we know


A = 2*(B+C)


A = 2*(24+C)


A = 2*24+2C


A = 48 + 2C


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All 3 angles add to 180 degrees, so A+B+C = 180


A+B+C = 180


A+24+C = 180 ... plug in B = 24


48+2C+24+C = 180 ... plug in A = 48+2C, now solve for C


48+2C+24+C = 180


72+3C = 180


3C = 180-72


3C = 108


C = 108/3


C = 36


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Use this to find A


A = 48+2C


A = 48+2*36 ... plug in C = 36


A = 48+72


A = 120