A ball is thrown at 20 m/s on the Moon, where g = 1.6 m/s²…

Check. The largest value of $\sin 2\theta$ is 1, at $\theta = 45$. Then $R = 400 / 1.6 = 250$ m. A range above 200 m needs $\sin 2\theta > 0.8$, so $2\theta$ between 53.1 and 126.9 degrees, so $\theta$ between 26.6 and 63.4 degrees. Of the multiples of 5, these are 30, 35, 40, 45, 50, 55 and 60: seven angles.