Plane angle and solid angle have:

1. Plane angle is defined as $\text{arc/radius}$. Unit: Radian. Dimensions: $[L]/[L]=[M^0{L}^0{T}^0]$.2. Solid angle is defined as ${\text{area/radius}}^2$. Unit: Steradian. Dimensions: $[L^2]/[L^2]=[M^0{L}^0{T}^0]$.Both are dimensionless quantities but have specific units.