### Theory:

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.
The sum of all the exterior angles of a polygon is $$360°$$.
Geometrical approach:
When all of the angles of a convex polygon converge or pushed together, they form one angle called  one complete turn (Perigon angle), which measures $$360$$ degrees.

If the sides of the convex polygon are increased or decreased, the sum of all of the exterior angles is still $$360$$ degrees. More sides can be added to the polygon and they will still form $$360°$$.

Therefore, the number of sides does not change the sum of the exterior angles of a convex polygon.
Algebraic approach:
For any polygon, exterior angle $$+$$ interior adjacent angle $$= 180°$$

So, if the polygon has n sides, then:

Sum of all exterior angles $$+$$ Sum of all interior angles $$= n × 180°$$

So, the sum of all exterior angles $$= n × 180°$$ $$-$$ Sum of all interior angles

Sum of all exterior angles $$= n × 180° - (n -2) × 180°$$

$$=$$ $$n × 180°$$ $$- n × 180°$$ $$+ 2 × 180°$$

$$=$$ $$180°n$$ $$- 180°n$$ $$+ 360°$$

$$= 360°$$

Therefore, we conclude that the sum of all the exterior angles of the polygon having $$n$$ sides $$=$$ $$360°$$.
We know that 'a regular polygon is a polygon whose all sides and all angles are equal. Thus, a regular polygon is both equiangular and equilateral'.
As all the angles are equal in a regular polygon, each exterior angle of a polygon is $\frac{360\mathrm{°}}{n}$, where $$n$$ is the number of sides.
Alternatively, we can find the number of sides of a regular polygon if we know the exterior angle of it.
The number of sides of a regular polygon $$n =$$$\frac{360\mathrm{°}}{\mathit{each}\phantom{\rule{0.147em}{0ex}}\mathit{exterior}\phantom{\rule{0.147em}{0ex}}\mathit{angle}}$.
Important!
• The sum of measures of all the exterior angles of a polygon is $$360°$$.
• Each exterior angle of a regular polygon is $\frac{360\mathrm{°}}{n}$, where $$n$$ is the number of sides.
• The number of sides of a regular polygon $$n =$$ $\frac{360\mathrm{°}}{\mathit{each}\phantom{\rule{0.147em}{0ex}}\mathit{exterior}\phantom{\rule{0.147em}{0ex}}\mathit{angle}}$.
• The sum of all the exterior angles formed by producing the sides of a convex polygon in the same order is equal to four right angles ($$4×90°$$ $$= 360°$$).