Question

The sum of the interior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon.

• A. $10$
• B. $12$
• C. $8$
• D. $7$

Answer 1

The correct option is A $10$

The sum of the interior angles of a polygon is four times the sum of its exterior angles.
The sum of the exterior angles of a polygon is always equal to ${360}^o$.
The sum of the interior angles of polygon = $180(n-2)$
=> $180(n-2)=4\times 360$
=> $n-2=8$
=> $n=10$
Number of sides in the polygon = $10$