Question

Mark (✓) against the correct answer
In a ∆ABC, If A − B = 33° and B − C = 18°, then ∠B = ?

(a) 35°
(b) 55°
(c) 45°
(d) 57°

Answer 1

$$\begin{gathered} \left(\mathrm{b}\right)55° \\ \begin{array}{l}\text{In}△\text{ABC:}\\ \text{A+B+C}=180{°}^{}...\left(\mathrm{i}\right)\\ Given,A-B=33°\end{array} \\ A=33°+B...\left(\mathrm{ii}\right) \\ \mathrm{B}-\mathrm{C}=18° \\ \mathrm{C}=\mathrm{B}+18°...\left(\mathrm{iii}\right) \\ \mathrm{Putting}\mathrm{the}\mathrm{value}s\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{in}\mathrm{equation}\left(\mathrm{i}\right): \\ \Rightarrow \mathrm{B}+33°+\mathrm{B}+\mathrm{B}-18°=180° \\ \Rightarrow 3\mathrm{B}=180°-15 \\ \Rightarrow \mathrm{B}=\frac{165°}{3}=55° \end{gathered}$$