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Z is 58 degrees, X is 58 degrees, and Y is 122 degrees. Y is an alternate interior angle to the given degree which means that Z should be 58 degrees to make that line a complete 180 degrees and X is an alternate interior angle to Z
we can get z because every straight line is 180 degrees, and 180-122= 58 degrees for z
we can then get y with that same routine, 180-58= 122 degrees for y
lastly, using those steps again, we know x is 58 degrees