Question 491280
Let
a = longest
b = middle
c = smallest
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Set up our equations.
-a +b + c =  16
3a - 3b -c = 0
a + b + c = 150
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multiply 1 * 3;add 1 to 2
-a +b + c =  16
      2c = 48
a + b + c = 150
c = 24 
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plug c into 1 and 3, 
-a +b + 24=  16
      2c = 48
a + b + 24= 150
multiply 1 by -1, add 1 to 3
-a +b + 24=  16
      2c = 48
 2a +  0= 134
a = 67 degrees.
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Solve for b.
67 + 24 = 91 ; 150 - 91 = 59
b = 59 degrees.
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a = 67 degrees.
b = 59 degrees.
c = 24 degrees.
Now, to check the system.
59 + 24 = 83; 83 - 16 = 67.
67 - 59 = 8; 8*3 = 24, which is the smallest angle.
67 + 59 + 24 = 150. 
This system does check.
Cleomenius.