An interior angle of a regular polygon is 5 times its exterior angle. Then, the number of sides of the polygon is [SSC (CGL) Mains 2014] |
A) 14
B) 16
C) 12
D) 18
Correct Answer: C
Solution :
Let the measure of exterior angle be \[x{}^\circ .\] |
Then, measure of interior angle \[=5x{}^\circ \] |
Now, |
Interior angle + Exterior angle \[=180{}^\circ \] |
\[\Rightarrow \] \[5x{}^\circ +x{}^\circ =180{}^\circ \] |
\[\therefore \] \[x{}^\circ =\frac{180}{6}=30{}^\circ \] |
\[\therefore \]Total sides of polygon |
\[=\frac{360{}^\circ }{\text{Exterior}\,\,\text{angle}}=\frac{360{}^\circ }{30{}^\circ }=12\] |
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