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I have 1000+ irregular shaped polygons where I would like to determine the orientation (azimuth) of their long axis. The polygons overlap in a few cases, if that matters. I am using the Minimum Bounding Geometry (Data Management) tool with the "Convex Hull" geometry type. When I run the tool, the resulting attribute table does not list anything except the length, area, and original feature ID -- not the MBG_Apod information and orientation as described here.

Why is this occurring and how can I fix it?

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Turn them on here. The red line.

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