The angle which the rough inclined plane makes with the horizontal when the body placed on it just starts sliding down is called

The angle at which the body just starts to slip is when frictional force is equal to the component of weight along the incline.

$\mathrm{mgsin\theta }=\mathrm{\mu mgcos\theta }\Rightarrow \mathrm{tan\theta }=\mathrm{\mu }\Rightarrow \mathrm{\theta }={\tan }^{-1}\left(\mathrm{\mu }\right)$

The angle at which the body just starts sliding is called angle of repose.