Plane angle and solid angle have :

Units but no dimensions Dimensions but no units No units and no dimensions Both units and dimensions

Units but no dimensions

Plane angle = \(\frac{Arc}{Radius}\) = \(\frac{[L]}{[L]}\)  unit : radians Solid angle = \(\frac{Area}{Radius^2}\) = \(\frac{[L^2]}{[L^2]}\)  unit : steradian