A) 5
B) 6
C) 7
D) 8
Correct Answer: B
Solution :
[b] Here, (interior angle) - (exterior angle) \[=60{}^\circ \] \[\Rightarrow \] \[\frac{(n-2)\times 180{}^\circ }{n}-\frac{360{}^\circ }{n}=60{}^\circ \] \[\Rightarrow \] \[\frac{1}{n}[(n-2)\times 180{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \] \[\frac{1}{n}[180{}^\circ n-360{}^\circ -360{}^\circ ]=60{}^\circ \] \[\Rightarrow \] \[180{}^\circ n-60{}^\circ n=720{}^\circ \] \[80{}^\circ n-60{}^\circ n=720{}^\circ \] \[120{}^\circ n=720{}^\circ \] \[n=6\] Therefore, the polygon contains 6 sides and it is called hexagon. |
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