Question

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In a ∆ABC, if ∠A + ∠B = 65° and ∠B +∠C = 140°. Then, = ∠B?

(a) 25°
(b) 35°
(c) 40°
(d) 45°

Answer 1

$$\begin{gathered} \left(a\right)25° \\ \mathrm{Given}: \\ \angle A+\angle B=65° \\ \angle A=65°-\angle B...\left(i\right) \\ \angle B+\angle C=140° \\ \angle C=140°-\angle B...\left(ii\right) \\ \mathrm{In}∆\mathrm{ABC}: \\ \angle A+\angle B+\angle C=180° \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}\angle \mathrm{B}\mathrm{and}\angle \mathrm{C}: \\ \Rightarrow 65°-\angle B+\angle B+140°-\angle B=180° \\ \Rightarrow -\angle B=180°-205° \\ \Rightarrow \angle B=25° \end{gathered}$$