I have a shapefile that shows up in QGIS and ArcGIS correctly.
But when I inspect the attributes of the layer it does not have latitude or longitude.
I need to extract the coordinate system so I'm looking for the lat/longs using QGIS.
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That's what shapefiles do: keep the coordinates in a binary where you cannot see them. In qgis go to the field calculator, ad a field "x": double, length 12 with 8 precision, and then write "$x" in the calculator, the same for "y"; if you want the nodes of a polygon or a line, first extract them (there's an option in the toolbox), then do the field calculator procedure.