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Explain why 0 degrees longitude and 180 degrees longitude are not designated east or west?

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0 degrees longitude does not have a designation of east or west because it behaves like a mathematical zero. It is neither positive nor negative. It is simply the start. Longitudes run through the north and south poles. Therefore, 0 degrees longitude is actually on the same line of longitude on the other side of the world which is 180 degrees longitude. Since all the longitude lines work like this, 180 degrees is the highest degree of longitude that you can have. Here is where it behaves just like 0 degrees because it cannot be any larger than 180 degrees. There is no need to say whether it is east or west then.
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What place is designated as 0 degrees longitude?

0 degrees longitude, known as the Prime Meridian is a line running from the North Pole to the South Pole that passes through Greenwich England.

What are the lines of longitude at 180 and 0 degrees?

-- The "Prime Meridian" marks zero longitude. -- The "180 th meridian" marks 180° longitude. The International Dateline is either on or relatively near the 180 th me

Why is 0 degrees and 180 degrees not designated east or west?

Simply because it doesn't matter in either case. -- Zero east or zero west puts you on the Prime Meridian either way. (Beginning on the Prime Meridian, you may travel 0°