Question

The sum of the interior angles of a polygon is three times the sum of its exterior angles. The number of sides of the polygon is:

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is D $8$

Let there be ${}^{\prime }{n}^{\prime }$ sides of the polygon.

Thus, each exterior angle $=\frac{360}{n}$

Or, Sum of exterior angles $={360}^o$

Sum of interior angles $=(2n-4){90}^o$

It is given, sum of interior angles $=$ 3(Sum of exterior angles)

Thus, $(2n-4){90}^o=3\left({360}^o\right)$

$\Rightarrow n-2=6$

$\Rightarrow n=8$