SOLUTION: In a triangle, angle A is 60 percent of angle C, and angle B is 150 percent of angle A. How many degrees does the smallest angle of the triangle measure?

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Question 694162: In a triangle, angle A is 60 percent of angle C, and angle B is 150 percent of angle A.
How many degrees does the smallest angle of the triangle measure?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a triangle, angle A is 60 percent of angle C, and angle B is 150 percent of angle A.
How many degrees does the smallest angle of the triangle measure?
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Let angle C be x degrees
Then angle A is 0.6x degrees
And angle B is 1.5(0.6x) = 0.9x degrees
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Equation:
x + 0.6x + 0.9x = 180 degrees
2.5x = 180 degrees
x = 72 degrees (measure of C)
0.6x = 43.2 degrees (measure of A)
0.9x = 64.8 degrees (measure of B)
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Cheers,
Stan H.
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Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
In a triangle the sum of angles is A%2BB%2BC=180 degrees.

if angle A is 60 percent of angle C,than
A=%2860%2F100%29C.....=>...A=0.60C

and if angle B is 150 percent of angle A, than
B=%28150%2F100%29A....=>...B=1.5%280.60C%29=>...B=0.9C%29
so, plug it in A%2BB%2BC=180
0.60C%2B0.9C%2BC=180.....solve for C
2.5C=180
C=180%2F2.5
highlight%28C=72%29
=>...A=0.60C
A=0.60%2A72
highlight%28A=43.2%29
=>...B=0.9C%29
B=0.9C%29
B=0.9%2A72%29
highlight%28B=64.8%29%29
so, the smallest angle of the triangle measure highlight%2843.2%29