A solid angle ($\Delta \Omega$) is defined as the ratio of the intercepted area ($\Delta A$) of a spherical surface to the square of its radius ($r^2$), mathematically expressed as $\Delta \Omega = \Delta A/r^2$ . Since both the area and the square of the radius have dimensions of $[L^2]$, the solid angle is a dimensionless quantity $[M^0 L^0 T^0]$ .

Similarly:

1. Angle (Plane Angle) is the ratio of arc length ($ds$) to radius ($r$), making it dimensionless ($[L]/[L]$) .
2. Strain is defined as the ratio of the change in a dimension to the original dimension (e.g., $\Delta L/L$), and thus it also has no dimensions .

Other quantities mentioned have dimensions: stress has dimensions of $[ML^{-1}T^{-2}]$ , arc length is a distance $[L]$ , and angular speed has dimensions of $[T^{-1}]$ . Therefore, strain and angle are the only quantities provided that are dimensionless like the solid angle.