The hybridisation of nitrogen atom in amines is

Let $\mathrm{R}-{\mathrm{NH}}_2$ be the amine.

We know that,

Number of hybrid orbitals $=$ number of sigma bonds $+$ number of lone pairs

$\Rightarrow$ number of sigma bonds $=1\mathrm{R}-\mathrm{N}$ bond $+2\mathrm{N}-\mathrm{H}$ bonds $+1$ lone pair $=4=$ number of hybrid orbitals

Thus, hybridisation $={\mathrm{sp}}^3$