In a △ABC=∠C=3∠B=2(∠A+∠B),then ∠B=?(a) 20∘(b) 40∘(c) 60∘(d) 80∘
Let ∠C=3∠B=2(∠A+∠B)=x
∠C=x, -----(1)
3∠B=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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