The other method is to create two fields in the polygon layer. (type Double) to hold the x and y values.
If the layer projection is different from the xy values you want to get, you can set the dataframe projection to the desired one.
Then open the table and right click on the new X filed. Choose calculate Geometry.
Choose X coordinate of Centroid, and use the coordinate system of the dataframe,
Click ok.
Do the same for the Y field.