Question

The sum of the exterior angles of a hexagon is?

• A. ${360}^{\circ }$
• B. ${540}^{\circ }$
• C. ${720}^{\circ }$
• D. none of these

Answer 1

The correct option is A ${360}^{\circ }$

Number of sides in hexagon $=6$
Sum of the interior angles of a polygon$=(n-2)\pi$
$n\left(InteriorAngle\right)=(n-2)\pi$
$\Rightarrow$ Interior Angle $=\frac{4}{6}\pi$

Interior Angle $={120}^{\circ }$
Exterior Angle $=180-$Interior Angle
$\Rightarrow$ Exterior angle $={60}^{\circ }$
Sum of Exterior angle $=6\times$ Exterior Angle $={360}^{\circ }$