Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-39

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

\[=\frac{360{}^\circ }{\text{Exterior}\,\,\text{angle}}=\frac{360{}^\circ }{30{}^\circ }=12\]