SOLUTION: The sum of the measures of the angles of a triangle is 180 degrees. The smallest angle of the triangle has a measure of 2/3 the measure of the second smallest angle. The largest

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Question 952642: The sum of the measures of the angles of a triangle is 180 degrees. The smallest angle of the triangle has a measure of 2/3 the measure of the second smallest angle. The largest angle has a measure that is 30 degrees less than three times the measure of the second smallest angle. Determine the measure of each angle
Answer by macston(5194) About Me  (Show Source):
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M=Middle angle; S=smallest angle=(2/3)M; L=largest angle=3M-30 degrees
S+M+L=180 degrees Substitute for S and L.
2/3(M)+M+3M-30 degrees=180 degrees Add 30 degrees to each side.
(14/3)M=210 degrees Multiply each side by 3/14
M=630/14=45 degrees ANSWER 1: The middle angle is 45 degrees.
S=2/3(M)=2/3(45 degrees)=30 degrees ANSWER 2: The small angle is 30 degrees.
L=3M-30=3(45 degrees)-30 degrees=105 degrees ANSWER 3: The large angle is 105 degrees.
CHECK:
S+M+L=180 degrees
30 degrees+45 degrees+105 degrees=180 degrees
180 degrees=180 degrees