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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

The correct option is (b).

Let A=x° and B=y°
C=3B=3y°
Now, A+B+C=180°
⇒ x + y + 3y = 180
⇒ x + 4y = 180 ...(i)
Also, C=2A+B
⇒ 3y = 2(x + y)
⇒ 2x − y = 0 ...(ii)
On multiplying (ii) by 4, we get:
8x − 4y = 0 ...(iii)
On adding (i) and (iii) we get:
9x = 180 ⇒ x = 20
On substituting x = 20 in (i), we get:
20 + 4y = 180 ⇒ 4y = (180 − 20) = 160 ⇒ y = 40
∴ x = 20 and y = 40
∴​ B=y°=40°

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