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Question

In a ABC=C=3B=2(A+B),then B=?(a) 20(b) 40(c) 60(d) 80


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    Solution

    Let C=3B=2(A+B)=x
    C=x, -----(1)
    3B=x
    B=x/3----(2)
    2(A+B)=x
    A+B=x/2
    A=x/2 -B
    A=x/2-x/3-----(3)
    sum of the three angles in a triangle is 180degree
    A+B+C=180
    x/2-x/3+x/3+x=180[from(1),(2),(3)]
    (3x-2x+2x+6x)/6=180
    9x/6=180
    x=180*6/9
    x=20*6
    x=120

    therefore
    A= x/2-x/3=120/2-120/3=60-40=20
    B=x/3=120/3=40
    C=x=120

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