A) \[\frac{7\pi }{12}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{5\pi }{6}\]
D) \[\frac{\pi }{2}\]
E) \[\frac{\pi }{3}\]
Correct Answer: D
Solution :
\[30{}^\circ =30{}^\circ \times \frac{\pi }{180}rad=\frac{\pi }{6}\] Let angle be \[a,\text{ }a+d,\text{ }a+2d\] Now, \[3a+3d=\pi \] \[\Rightarrow \]\[3\frac{\pi }{6}+3d=\pi \]\[\Rightarrow \]\[d=\frac{1}{3}\left( \pi -\frac{\pi }{2} \right)=\frac{\pi }{6}\] \[\therefore \]Greatest angle\[=\frac{\pi }{6}+2.\frac{\pi }{6}=\frac{3\pi }{6}=\frac{\pi }{2}\]
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