A solid angle is measured in steradians (sr), which is a dimensionless unit representing the ratio of an area to the square of the radius from the center of a sphere. Angles, measured in radians, are also dimensionless, defined as the ratio of arc length to radius. The discussion emphasizes that while radians and steradians are both dimensionless, they serve different purposes in geometry, with radians used for plane angles and steradians for solid angles. The use of "rad" as a unit is discouraged, as it can lead to confusion; instead, angles should simply be expressed as numbers. Clarity in communication is essential, especially when distinguishing between different types of angles.