If I'm doing my math correctly, Io covers about 0.06% as many degrees of our vision from Earth as the moon does. (I'm not good at this math, but I'm trying.)
The moon and Io are roughly the same diameter, so you can just divide Io's distance by the moon's distance to get the ratio of their perceived size without futzing with angles or geometry.
Io Diameter 2263.8 miles
Jupiter Distance to Earth 444000000 miles
Perp / Base 0.000005098648649
Radians 0.000005098648649
Degrees 0.0002922792219
Arc Seconds 1.052205199
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Moon Diameter 2159.1 miles
Moon Distance to Earth 238900 miles
Perp / Base 0.009037672666
Radians 0.009037426614
Degrees 0.5180690416
Arc Seconds 1865.04855