Question

In a $∆ABC,\angle C=3\angle B=2(\angle A+\angle B),\mathrm{then}\angle \mathrm{B}=?$
(a) 20°
(b) 40°
(c) 60°
(d) 80°

Answer 1

The correct option is (b).

Let $\angle A=x°and\angle B=y°$
∴ $\angle C=3\angle B=\left(3y\right)°$
Now, $\angle A+\angle B+\angle C=180°$
⇒ x + y + 3y = 180
⇒ x + 4y = 180 ...(i)
Also, $\angle C=2\left(\angle A+\angle B\right)$
⇒ 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
∴​ $\angle B=y°=40°$