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How to find the unknown coordinates reference system for my map data

Kofi_Lartey

I have several shapesfiles which perfectly overlay but the coordinates reference system is unknown. I need to overly these with other data in a differetn coordinate system. The coordinate extent is quite unique. I tried initially to overlay with several projected and geographic coordinates systems associated with the area out of which two showed very close displacement (about 60m). Next i tried different datum with one of the 'promising' coordinates reference systems (a geographic coordinates system) and also change the units but same results. Attached is a clip of two of the coordinate extents. I am yet to try the

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