The measure of the exterior angle of a regular polygon is given by the formula [tex]\dfrac{360}{n}[/tex] where [tex]n[/tex] is the number of sides.
To find the number of sides of a polygon with the exterior angle measuring [tex]1^{\circ}[/tex] we have to solve the equation [tex]\dfrac{360}{n}=1[/tex].
[tex]\dfrac{360}{n}=1|\cdot n\\
n=360
[/tex]
It has 360 sides.
