In a ΔABC, ∠C = 3 ∠B = 2 (∠A + ∠B), then ∠B = ?A. 20°B. 40°C. 60°D. 80°

Let us assume, A = xo and B = yo

A = 3 B = (3y)o

We know that, sum of all sides of the triangle is equal to 180o

A + B + C = 180o

x + y + 3y = 180o

x + 4y = 180o (i)

Also we have, C = 2 ( A + B)

3y = 2 (x + y)

2x – y = 0 (ii)

Now, by multiplying (ii) by 4 we get:

8x – 4y = 0 (iii)

And adding (i) and (iii), we get

9x = 180o

x = 20

Putting the value of x in (i), we get

20 + 4y = 180

4y = 180 – 20

4y = 160

y = 40

B = y = 40o

Hence, option B is correct

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