Question

The interior angle of a regular polygon with $n$ sides is $6$ times that of an exterior angle of a regular polygon with $\frac{3}{2}n$ sides. Then $n$ equals

• A. $12$
• B. $20$
• C. $10$
• D. $18$

Answer 1

Answer: (C)

$10$

Interior angle of n sided polygon $=$ $\frac{n-2}{n}\times 180$
Exterior angle of $\frac{3}{2}n$ sided polygon $=$ $\frac{360}{\frac{3n}{2}}$
Now, $\frac{n-2}{n}\times 180$ $=$ $6\times \frac{360}{\frac{3n}{2}}$
$\Rightarrow n-2=8$
$\Rightarrow n=10$