Can a regular polygon have an exterior angle of $50^{\circ}$?
Can a regular polygon have an exterior angle of $50^{\circ}$?
Yes, with $5$ sides
Yes, with $7$ sides
No, because $360^{\circ}$ is not divisible by $50^{\circ}$
Yes, with $8$ sides
Solution
For a regular polygon $n = \dfrac{360}{\text{ext.angle}}$ must be a positive integer. $\dfrac{360}{50} = 7.2$, not an integer. So no such regular polygon exists.