Earlier:
By "angle that a dipole radiates" do you mean the
angle of maximum radiation? If so, it depends upon
the height and length of the dipole among other things.
______________

To be more exact, a linear (1/2-wave) dipole produces maximum radiation at
all angles perpendicular to its center.

But as suggested by the quote above, radiation from the driven element along
with the distance, geometry, and electrical characteristics of nearby
conductors (including the earth) will determine the final pattern of the
radiated signal.

R. Fry