Theory:

A plane angle is an angle at the intersection of two straight lines or two planes. It has two dimensions. Radian is the SI unit of plane angle, and it is denoted as 'rad'.
 
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The angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle is known as radian.
 
π \(radian\) \(=\) \(180°\)
 
Then, \(1\) \(radian\) \(=\)  180°π
 
Radians are used to measure the angles. A value in terms of radian can be converted into degrees and vice-versa.
Solid angle
A solid angle is an angle formed by three or more planes intersecting at a common point. It is also known as the angle formed at the vertex of the cone.
Steradian is the unit of solid angle, and it is denoted as 'sr'.
 
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Steradian is a solid angle at the centre of a sphere subtended by a portion whose surface area is equal to the square of the radius of the sphere. It has three dimensions.
 
Earlier, the plane angle and the solid angle was considered supplementary quantities. But, they were changed to derived quantities in \(1995\).