| The interior angle of a regular polygon exceeds its exterior angle by \[108{}^\circ .\] The number of sides of the polygon is |
| [SSC (CGL) Mains 2015] |
A) 16
B) 12
C) 14
D) 10
Correct Answer: D
Solution :
| Let the exterior angle be x. |
| \[\therefore \]Interior angle \[=x+108{}^\circ \] |
| \[\because \] \[x+x+108{}^\circ =180{}^\circ \]\[\Rightarrow \]\[2x=72{}^\circ \]\[\Rightarrow \]\[x=36{}^\circ \] |
| \[\therefore \]Number of sides\[=\frac{360{}^\circ }{36{}^\circ }=10\] |
| \[{{\left[ \because \text{number}\,\text{of}\,\text{sides}=\frac{\text{360 }\!\!{}^\circ\!\!\text{ }}{\text{exterior}\,\text{angle}} \right]}^{{}}}\] |
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