Question

If a regular polygon has one exterior angle measuring 1°, then it has_______ sides.

Answer 1

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

$\dfrac{360}{n}=1|\cdot n\\ n=360$

It has 360 sides.