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. $12$
• B. $19$
• C. $18$
• D. $16$

Answer 1

The correct option is C $18$

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