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The numbering systems for longitude and latitude are simply different expressions of a circle. Without these intersecting lines, there would be no way to precisely position any location on the globe.

Longitude measures distance east and west of the Prime Meridian -- 0 degrees, the line that essentially 'separates the Earth into two halves', except that its continuation -- the International Date Line -- 180 degrees, isn't straight, for political reasons.

Latitude measures distance north and south of the Equator -- 0 degrees, which indeed 'separates the Earth into two halves'.

Combining longitude and latitude, you can, indeed, find any location on our planet.

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Q: Why do lines of longitude run only 180 degree half circles around the earth while lines of latitude run in full 360 degree circles?
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