In a ΔABC, ∠C = 3 ∠B = 2 (∠A + ∠B), then ∠B = ?
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