SOLUTION: The measure of the second angle of a triangle is 12 degrees greater then three times the first angle. The measure of the third angle is 6 degrees less than twice the measure of the

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Question 28822: The measure of the second angle of a triangle is 12 degrees greater then three times the first angle. The measure of the third angle is 6 degrees less than twice the measure of the second angle. What are the measures of the three angles?

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Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
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The measure of the second angle of a triangle is 12 degrees greater then three times the first angle. The measure of the third angle is 6 degrees less than twice the measure of the second angle. What are the measures of the three angles?
Let the first angle be A degrees,
the second angle be B degrees and
the third angle be C degrees.
The second angle is 12 degrees greater than three times first angle.
B is 12 more than 3A
That is B= 3A+12 ----(1)
The third angle is 6 less than twice the second angle.
C is 6 less than 2B
C=2B-6 ----(2)
A,B and C being the angles of a triangle ABC,
we have A + B + C = 180 degrees. ----(*)
Using (1) and (2) in (*)
A +(3A+12)+(2B-6) =180
A+3A +12-6+2B=180
4A+6+2B=180
4A+2B= 180-6
4A+2B= 174
4A+ 2(3A+12) =174 using (1) and substituting for B in terms of A
4A+6A+24 =174
10A=174-24
10A = 150
A = 150/10 = 15
A= 15 in (1),then B= 3A+12 = 3X15+12 = 45+12 =57
Putting B= 57 in (2),
C=2B-6 = 2X57-6 = 114-6 = 108
Therefore the angles are 15 deg, 57 deg and 108 deg respectively.
Verification: Obviously they are adding up to 180 beautifully. Good