This is the animation of the Moon's position over Los Angeles, CA skies at 8 p.m. local (PDT) time from September 25 to September 27, 2015 (made with Sky Map Online):
As you can see, there isn't any way to describe its apparent movement with a single angular distance, whichever method you use. In astronomy, position of objects on the night skies is most commonly given by RA/Dec (Right Ascension and Declination), which places an object on the celestial sphere.
Unless we count the Supermoon Eclipse on September 27, 2015 (your time, September 28 UTC), one that won't occur again until October 8, 2033, or exactly one saros period since the last one, there wasn't anything else as extraordinarily dramatic about the Moon's movement on those nights as you describe. So what happened is most likely that measurements by your observations weren't taken precisely enough; Be it you didn't time your observations precisely, didn't measure Moon's position relative to some fixed direction from some fixed vantage point, didn't project its position onto your scale taking the curvature of the celestial sphere into account, or a bit of any or all of these.
The Moon, if observed at the same solar time from the same location, moves in apparent eastward direction (when it's visible and above the horizon, westwards when it's below the horizon, regardless if that's during day or night) roughly 13° per day, or, saying it otherwise, each day, at the same time, it will appear to lag for about an hour relative to its position a day before. Why? Simply because it completes one orbit around the Earth every 27.321582 days, so at exact same solar time the next day, it will be 360°/27.321582 or 13.18° more East. Its apparent movement during the same day is of course still East to West, because the Earth rotates on its axis towards East much faster than the Moon rotates around the Earth.
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