Question

The sum of all exterior angles of a polygon is __________.

Answer 1

Polygon:

1. A plane shape (two-dimensional) with straight sides. Examples: triangles, rectangles and pentagons.
2. We will consider the pentagon here to find the sum of its exterior angle. The pentagon can be drawn as

1. We know that the sum of all the interior angles in ant of the polygon is $180(\mathrm{n}-2)$where $\mathrm{n}$ is the number of sides present in the polygon.
2. Here the value of $\mathrm{n}$ is $5$ so the sum of all the interior angles is
   $1+2+3+4+5=180(5-2)=180\left(3\right)=540degrees\dots \dots \dots \dots \left(1\right)$
3. We know that linear angle is ${180}^{\circ }$ so, we can say that Angle $\mathrm{a}+$Angle $5=180$
4. Therefore there are five exterior angles in the polygon here,
5. Therefore the angle $\mathrm{a}=180–$angle $5$ which is nothing but $180–$ interior angle.
6. Similarly, we can find all the exterior angles.
7. So, the sum of exterior angles is $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}=5\left(180\right)–$sum of interior angles.
8. So, we do from (1) $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}=5\left(180\right)–540=900–540={360}^{\circ }$

Final answer:

The sum of all exterior angles of a polygon is ${360}^{\circ }$.