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When I open in QGIS a new project and I add a Openstreetmap Basemap, the Project CRS is set automatically to EPSG:3857.

I have a specific Shapefile representing a State boundary of an African country: when I import the file the software ask me to choose which CRS use. Selecting the same of the project (ESPG: 3857) the Shapefile is not aligned correctly. I tried to export the file, selecting the correct ESPG but the issue persist.

I also tried to Reproject layer, but doesn't change the outcome.

As you can see in the screenshot Ethiopia is shifted to the right, even the CRS of both Basemap, project and Shapefile are the same

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    Have you tried loading the original shape layer and choosing the native CRS of the file? – Erik Mar 6 at 8:13
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    Please have a look in the .prj file and share its contents. – Erik Mar 6 at 8:30
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    And you are wondering that QGIS doesn't know where to put your data. Can you get the .prj file from somewhere, or is the CRS of the shape somewhere mentioned by your data source? – Erik Mar 6 at 8:43
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    These are the only details I can find in the data source: West Bounding Coordinate: -1.4542158012618367 East Bounding Coordinate: 13.432354606946799 North Bouding Coordinate: 14.624264198458649 South Bounding Coordinate: 3.3791913158490394 datacatalog.worldbank.org/dataset/ethiopia-rain-patterns – high_point Mar 6 at 9:03
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    Solution below, but as a sidenote you might want to message the worldbank about the missing .prj file. – Erik Mar 6 at 9:07
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Since you provided the data source, I was able to verify the correct CRS of the data: EPSG 32637 - UTM Zone 37 N.

Before loading the data, set your project CRS to 32637. Then load the data and when asked for the CRS, tell it to use the same. Then save the data to a new location by right clicking it, this creates the missing .prj file automatically.

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