A) \[90{}^\circ \]
B) \[135{}^\circ \]
C) \[115{}^\circ \]
D) \[105{}^\circ \]
E) \[120{}^\circ \]
Correct Answer: E
Solution :
\[\because \]Longest side has largest angle opposite to it. \[\therefore \] \[\cos A=\frac{{{(2x+1)}^{2}}+{{({{x}^{2}}-1)}^{2}}-{{({{x}^{2}}+x+1)}^{2}}}{2({{x}^{2}}-1)(2x+1)}\] \[=\frac{-(2{{x}^{3}}+{{x}^{2}}-2x-1)}{2(2{{x}^{3}}+{{x}^{2}}-2x-1)}=-\frac{1}{2}\] \[\Rightarrow \] \[\cos A=\cos 120{}^\circ \] \[\Rightarrow \] \[A=120{}^\circ \]
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