Question

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

• A. $3$
• B. $9$
• C. $6$
• D. $8$

Answer 1

Answer: (D)

$8$

The sum of interior angles of a regular polygon is three 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,
${180}^o(n-2)=3\times {360}^o$
$=>(n-2)=6$
$=>n=8$
Number of sides of the polygon = 8