10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Pair of Linear Equations in Two Variables

  • question_answer In a \[\Delta ABC,\] \[\angle C=3\angle B=2(\angle A+\angle B).\]. The three angles will be ____.

    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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