Question

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

(a) 35°
(b) 55°
(c) 45°
(d) 57°

Answer 1

$$\begin{gathered} \left(b\right)55° \\ \begin{array}{l}\text{In}△\text{ABC:}\\ \angle \text{A}+\angle \text{B}+\angle \text{C}={180}^0...\left(i\right)\\ \text{Given:}\\ \angle \text{A}-\angle \text{B}={33}^0=>\angle \text{A}=\angle \text{B}+{33}^0...\left(ii\right)\\ \angle \text{B}-\angle \text{C}={18}^0=>\angle \text{C}=\angle \text{B}-{18}^0...\left(iii\right)\\ \text{Using}\left(ii\right)\text{and}\left(iii\right)\text{in equation}\left(i\right):\\ =>\angle {\text{B + 33}}^0+\angle \text{B +}\angle \text{B}-{18}^0={180}^0\\ \text{=> 3}\angle {\text{B + 15}}^0={180}^0\\ \text{=> 3}\angle {\text{B = 165}}^0\\ \text{=>}\angle \text{B =}\frac{{165}^0}{3}={55}^0\\ \\ \end{array} \end{gathered}$$