Answer
The angular width of the Milky Way from a nearby galaxy is $\phi = 4.2\times 10^{-2}~radians$
This angular width is 4.6 times larger than the angular width of the moon as observed from the Earth.
Work Step by Step
We can use this equation to find the angular width of the Milky Way from the nearest large galaxy:
$D = \frac{d}{\phi}$
(Note that D is the distance to the galaxy, d = the width of the Milky Way, and $\phi$ is the angular width measured in radians.)
$\phi = \frac{d}{D} = \frac{10^5~ly}{2.4\times 10^6~ly}$
$\phi = 4.2\times 10^{-2}~radians$
We can use the same equation to find the angular width of the moon from the Earth. Note that $d=3500~km$ (the moon's diameter) and $D = 385,000~km$ (the average distance to the moon):
$\phi = \frac{d}{D} = \frac{3500~km}{385,000~km}$
$\phi = 9.1 \times 10^{-3}~radians$
We can compare the two angular widths:
$\frac{4.2\times 10^{-2}~radians}{9.1 \times 10^{-3}~radians} = 4.6$
The angular width of the Milky Way from a nearby galaxy is 4.6 times larger than the angular width of the moon as observed from the Earth.
