Question

why is anticlockwise moment taken positive and clockwise negative

Answer 1

This is because of the right hand screw rule.
If u move ur fingers in anti clockwise direction the thumb points upwards indicating positive direction.
If u move ur fingers in clockwise direction the thumb points downwards indicating negative direction.

Answer 2

Answer: Normally we take the positive X axis as reference. When moving UP (positive) the movement is in the anticlockwise direction. This is the logic behind taking anticlockwise as positive and clockwise as negative.