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I have a shapefile delineating 563 districts, I want to create a field that indicates whether the road network (red line) intersects the district or not.

How do I do this?

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I assume you are working on ArcGIS desktop. I think they easies way to do it is to first create empty field (let's call it "Intersect") in your polygon layer.

After that use "Select By location" tool.

Inside this tool select from polygon layer all polygons that intersect with your line layer. Then in your attribution table use field calculator on your "intersect" column and add number or value.

Sorry but i am away from my PC so i can't add screenshot's.

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