Statement-1 : Plane angle is a dimensionless quantity.
Statement-2 : All supplementary quantities are dimensionless.
A. Statement 1 and statement 2 is correct and statement 2 is a correct explanation of statement 1.
B. Statement 1 and statement 2 is correct and statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true and statement 2 is false
D. Statement 1 false and statement 2 is true

Hint :Supplementary units are the dimensionless units that are used along with the base units to form derived units in the international system.
The class of supplementary contains only two purely geometrical units, which is the radian and the steradian.

Complete Step By Step Answer:
Plane angle has radian or unit which does not come under SI or derived units. Units of plane angles radian and scale angles steradian are dimensionless quantities hence they have been put in a separate category of supplementary units. So, the reason is correct.
Therefore, option A is the correct option i.e., Statement 1 and statement 2 is correct but statement 2 is not a correct explanation of statement 1.

Note :
Let’s talk about all the options – Option B is an incorrect option. Because from the above explanation we can say that statement 2 is the correct explanation.
Let’s talk about option C.
Option C – it is also an incorrect option because “Supplementary units that are radian and steradian are dimensionless units. They are assumed standards and don’t have a physical meaning they are separate from fundamental units.”
Option D statement 1 false and statement 2 is true
It is also an incorrect option because plane angle comes under supplementary quantities or units which are dimensionless units.
So, statement 1 and 2 both are true.