At what angle does Earth travel along its orbit after 29.5 days?

If one were to assume a circular orbit (actually earth orbit is slightly elliptical) then theta = 29.5 / 365.25 * 360 = 29 deg

The angle of the radius of the orbit would change by 29 deg in 29.5 days

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.