Sides!!!!

Question

+1

1053

1

+818

How many polygons have interior angles of integral measure?

mathtoo Dec 25, 2018

+199

+2

Best Answer

We first go by the exterior angle measure: $\frac{360}{n}$ .

Now, $n$ has to be a factor of $360$ , so we count how many factors this number has.

Since $360=2^3*3^2*5$ , we add one to each power, resulting in $4*3*2=24$ factors.

Finally, a polygon cannot have one or two sides; thus the answer is $24-2=\boxed{22}$ regular polygons.

azsun Dec 25, 2018

azsun · Answer 1 · 2018-12-25T06:01:31

We first go by the exterior angle measure: $\frac{360}{n}$ .

Now, $n$ has to be a factor of $360$ , so we count how many factors this number has.

Since $360=2^3*3^2*5$ , we add one to each power, resulting in $4*3*2=24$ factors.

Finally, a polygon cannot have one or two sides; thus the answer is $24-2=\boxed{22}$ regular polygons.