A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{5}\]
Correct Answer: C
Solution :
Let the four angles of a quadrilateral are \[{{(a-3d)}^{o}},{{(a-d)}^{o}},{{(a+d)}^{o}}\] and \[{{(a+3d)}^{o}}\] \[\therefore \] \[a-3d+a-d+a+d+a+3d={{360}^{o}}\] \[\therefore \] \[a={{90}^{o}}\] But the greatest angle is double the least, i.e. \[a+3d=2\times (a-3d)\] \[=2a-6d\] \[\therefore \] \[9a=2a-a\] \[=a\] \[={{90}^{o}}\] \[\therefore \] \[d=\frac{90}{9}={{10}^{o}}\] \[\therefore \] Least angle \[=a-3d\] \[={{90}^{o}}-3\times {{10}^{o}}\] \[={{60}^{o}}\] \[=\frac{\pi }{3}\]
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