Question

The sum of the exterior angles of a hexagon is
A. $${360}^0$$
B. $${540}^0$$
C. $${720}^0$$
D. None of these

Answer 1

Hint:First of all, find the sum of interior angles of the hexagon and so that we can find each interior angle. Find the angle of each exterior angle of the hexagon to find the sum of the exterior angles of the hexagon.

Complete step-by-step answer:
Number of sides in a hexagon $$n=6$$ as shown in the below figure:

We know that sum of interior angles of a polygon $$=\left(n-2\right)\pi$$
So, sum of interior angles of the hexagon $$=\left(6-2\right)\pi =4\pi$$
If the sum of 6 interior angles is $$4\pi$$, then one angle is equal to $${\displaystyle \frac{4\pi }{6}}={120}^0$$
We know that the sum of interior and exterior angle is equal to $${180}^0$$ i.e.,
Interior angle + Exterior angle = $${180}^0$$
Exterior angle = $${180}^0-$$ Interior angle
                          = $${180}^0-{120}^0={60}^0$$
As there are 6 exterior angles in a hexagon, the sum of the exterior angles in hexagon is $$6\times {60}^0={360}^0$$
Hence the sum of the exterior angles in the hexagon is $${360}^0$$
Thus, the correct option is A. $${360}^0$$

Note:Hexagon is one of the polygons. Hexagon has 6 equal sides. The sum of interior and exterior angle is equal to $${180}^0$$. The sum of interior angles of a polygon is equal to $$\left(n-2\right)\pi$$ where $$n$$ is the number of sides of the polygon.