Plane angle and solid angle have :

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(D) Plane angle is defined as the ratio of arc length to radius $(d	heta = ds/r)$. Since both arc length and radius have the dimension of length $(L)

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Units but no dimensions

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(D) Plane angle is defined as the ratio of arc length to radius $(d	heta = ds/r)$. Since both arc length and radius have the dimension of length $(L)$,the dimension of plane angle is $[L^1/L^1] = [M^0 L^0 T^0]$,which is dimensionless. However,it has a unit,which is radian $(rad)$.Similarly,solid angle is defined as the ratio of the area of the spherical surface to the square of the radius $(d\Omega = dA/r^2)$. Since both area and the square of the radius have the dimension of length squared $(L^2)$,the dimension of solid angle is $[L^2/L^2] = [M^0 L^0 T^0]$,which is also dimensionless. However,it has a unit,which is steradian $(sr)$.Therefore,plane angle and solid angle have units but no dimensions.

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