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 243985: 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.
Found 2 solutions by solver91311, richwmiller:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the measure of angle B. Then is the measure of angle A, and is the measure of angle C. So:



Solve for to get angle B. Multiply the measure of B by 3 to get angle A. Subtract 16 from the measure of A to get C.

Or, you could let represent angle A. Then is the measure of angle B, and is the measure of angle C. So:



Or, you could let represent angle C. Then is the measure of angle A and is the measure of angle B. So:



Personally, I like the first way the best, but they all give the same answer in the end.

John
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
a=first angle
b=second angle
c=third angle
a=3b
a=16+c
solve for a
b=a/3
c=a-16
a+b+c=180
substitute
a+a/3+a-16=180
combine and reduce
2a +a/3=196
divide by 2
a+a/6=98
multiply by 6
6a+a=6*98
7a=6*98
7a=588
a=588/7
a=84
b=a/3=28
c=a-16=84-16=68
check
84+28+68=180
180=180
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