Question

The sum of interior angles of a polygon is eight times the sum of its exterior angles. How many sides does this polygon have?

• A. 15
• B. 17
• C. 12
• D. 18

Answer 1

The correct option is D 18

The sum of interior angles of a regular polygon is eight times 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,
${180}^o(n-2)=8\times {360}^o$
$=>(n-2)=16$
$=>n=18$
Number of sides of the polygon = 18