An object is projected in the air with initial velocity u at an angle θ . The projectile motion is such…

The maximum range is given by, $R_{\max }=\frac{u^2\sin 2\left(45°\right)}{g}=\frac{u^2}{ g}$.

For the range to be half of the maximum range,

$\frac{R_{max}}{2}=\frac{u^2}{2 g}=\frac{u^2\sin 2\theta }{g}$

$\Rightarrow \sin 2\theta =\frac{1}{2}$

$\Rightarrow 2\theta =30°\text{or} 2\theta =150°$

$\Rightarrow \theta =15°,75°$

Therefore, answer is $15 \text{or }75$