The idea here is to take the idea and play with it. Try turning it around.

That is, we just saw that if we start with the number of sides of a regular polygon, we can get an interior angle. If we start with an interior angle of a regular polygon, can we find the number of sides?

Every interesting solution leads to more problems. That is what makes mathematics fun!

What are some angle sums with no solution.

Can we create a regular polygon with interior angle>=179? How many sides would it need to have?

What would the number of sides against the interior angle value? What do you see?

Not all problems have a solution.