Question

The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

Answer: (B)

$6$

The sum of interior angles of a regular polygon is twice the sum of its exterior angles.
Sum of all interior angles of a regular polygon = ${180}^o(n-2)$ where $n=$ number of sides of polygon
Sum of all exterior angle of a regular polygon = ${360}^o$
According to question,
${180}^o(n-2)=2\times {360}^o$
$=>(n-2)=4$
$=>n=6$
Number of sides of the polygon $=6$