A) \[{{20}^{o}}\text{, }{{40}^{o}},\text{ }{{120}^{o}}\]
B) \[{{30}^{o}},\text{ }{{60}^{o}},\text{ }{{90}^{o}}\]
C) \[{{45}^{o}},\text{ 4}{{\text{5}}^{o}},\text{ }{{90}^{o}}\]
D) \[{{90}^{o}},\text{ 4}{{\text{0}}^{o}},\text{ 5}{{0}^{o}}\]
Correct Answer: A
Solution :
In a triangle, sum of angles is \[{{180}^{o}}\] \[\therefore \] \[\angle A+\angle B+\angle C={{180}^{o}}\] .....(1) \[\angle C=3\angle B\] ?...(2) and \[3\angle B=2\angle A+2\angle B\] \[\therefore \] \[\angle A=\frac{\angle B}{2}\] ??(3) From (1), (2) and (3), we get \[\frac{\angle B}{2}+\angle B+3\angle B={{180}^{o}}\] \[\Rightarrow \] \[\left( \frac{9}{2} \right)\angle B={{180}^{o}}\] \[\Rightarrow \] \[\angle A={{20}^{o}}\]
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