Question

The interior angle of a regular polygon is double the exterior angle. Then the number in the polygon is

• A. $6$
• B. $8$
• C. $9$
• D. None of these

Answer 1

The correct option is A $6$

Let the number of sides in the polygon is $n$

Let the measure of exterior angles be $x$ respectively.

$\therefore$ Measure of interior angle $=2x$

So,

$\Rightarrow$ $n\times 2x=(2n-4)\times {90}^o$

$\Rightarrow$ $nx=(n-2)\times {90}^o$ ----- ( 1 )

Again we know that,

$\Rightarrow$ $nx={360}^o$

$\Rightarrow$ $(n-2)\times {90}^o={360}^o$ [ From ( 1 ) ]

$\Rightarrow$ $n-2=4$

$\Rightarrow$ $n=6$

$\therefore$ The number of sides in the polygon are $6.$