SOLUTION: In any triangle, the sum of the measures of the angles is 180° . In ΔABC, ∢ A is three times as large as ∢ B and also 16° larger than ∢ C. Find the measure

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Question 243203: In any triangle, the sum of the measures of the angles is 180° . In ΔABC, ∢ A is three
times as large as ∢ B and also 16° larger than ∢ C. Find the measure of each angle.
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In any triangle, the sum of the measures of the angles is 180° . In ΔABC, ∢ A is twice as
large as ∢ B. ∢ B is 4° larger than ∢ C. Find the measure of each angle.
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
The setup of the problem tells us:
A + B + C = 180
A = 3B, so B = A/3
A = C+16, C = A-16
Substitute into basic formula:
A + A/3 + A-16 = 180
2A + A/3 = 196
Getting rid of the fractional A is next:

...
So we have:

Which can be simplified by multiplying both sides by 3.
7A = 3*196 = 588
Dividing both sides by 7, we have:
A = 84
...
Looking back to the equations we define:
B = A/3 = 84/3 = 28
and
C = A-16 = 68
...
To summarize:
A = 84
B = 28
C = 68
...
To check your work, check the solution to the fundamental equation.
Does A + B + C = 180?
84 + 28 + 68 = 180
So we have our answer.
...
Follow these same steps to answer your 2nd question.
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