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How many polygons have interior angles of integral measure?

Dec 25, 2018

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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.

Dec 25, 2018

#1
+192
+2

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