The distance to the lmc is about 160000 light-years, and the diameter of the galaxy is about 100000 light-years. So by trigonometry the apparent diameter would be about $2\arctan(0.5\times 100000/160000)=35^\circ$ And that is close enough to the quote value to be a difference in rounding.
The absolute magnitude of the milky way is quoted taken as -21.3 So a naive calculation of apparent magnitude based on a distance modulus of $5\log_{10}(160000/3.26 -1)=23.4$ would be $-21.3 + 23.4 = 2.1$. That is quite a long way from the quoted value. But note that calculating a magnitude of such a extended object isn't of much use instead you would normally consider surface brightness.