Question

If the sum of the interior angles of a regular polygon is five times the sum of its exterior angles, then the number of sides it has is

• A. 14
• B. 12
• C. 11
• D. 10

Answer 1

The correct option is B

12

Sum of interior angles of a polygon = $(n-2)\times {180}^0$

Sum of exterior angles of a polygon = ${360}^0$

Given that,

$(n-2)\times {180}^0=5\times {360}^0$

$(n-2)=\frac{5\times {360}^0}{{180}^0}$

$(n-2)=10$

$\Rightarrow n=12$