Question

In a certain polygon, the sum of the measures of all the interior angles is equal to twice that of the exterior angles. The polygon is a.

• A. Pentagon
• B. Hexagon
• C. Octagon

Answer 1

The correct option is B Hexagon

Given:
Sum of interior angles = $2\times$ the sum of exterior angles
[$n=$ number of sides of the polygon]
$⟹(n-2)\times {180}^{\circ }=2\times {360}^{\circ }$
$⟹(n-2)=\frac{2\times {360}^{\circ }}{{180}^{\circ }}$
$⟹(n-2)=2\times 2$
$⟹n=4+2=6$
$⟹$ polygon having $6$ sides, hence the polygon is hexagon.