Pearl, are you sure you have worded this properly? Should it say the
internal angle is 8 times the external angle?

Penny

Pearl wrote back

Yes I am sure

Pearl,

Look at Walter's response to Evelina about the exterior angles of a regular polygon. He gives a geometric argument to show that the exterior angles of a regular polygon with $n$ sides each measure $\large \frac{360}{n}$ degrees. Hence each interior angle measures $180 - \large \frac{360}{n}$ degrees. If each exterior angle is 8 times an interior angle then

\[\frac{360}{n} = 8 \times \left( 180 - \frac{360}{n} \right ).\]

Solve for $n.$

The problem I have is that $n$ is not an integer. That is why I asked you if you had worded the problem correctly. If the internal angle is 8 times the external angle then $n$ is an integer.

I hoe this helps,
Penny