Vertex Angles in a Regular Polygon

Investigate how the vertex angle of a regular polygon relates to its number of sides.



Find the measure of the vertex (blue) angle of the red isosceles triangle that can be used to rotate the triangle about its vertex to create a regular pentagon. What should the measure of the vertex angle be if you want to create a square, a regular hexagon, or a regular n-sided polygon?

Will any measure for this vertex angle in the isosceles triangle create a regular polygon? Explain why or why not.