SOLUTION: in triangle ABC angle A is twice as large as angle B and also 16 degrees larger than angle C. What are the measurements of the angles?

Question 659647: in triangle ABC angle A is twice as large as angle B and also 16 degrees larger than angle C. What are the measurements of the angles?

Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
A + B + C = 180degrees
A = 2B; B = A/2
A = 16 + C; C = A - 16
Substitute the second and third equation into the first equation
A + (A/2) + (A - 16) = 180
2A + A/2 = 180 + 16
2A + A/2 = 196
2A(2) + (A/2)(2) = 196(2)
4A + A = 392
5A = 392
A = 78.4degrees
Plug A into the second equation and third equation
A = 2B; B = A/2; B = 78.4/2 = 39.2
B = 39.2degrees
A = 16 + C; C = A - 16; C = 78.4 - 16 = 62.4
c = 62.4degrees

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