Does absolute value apply to angles?

The measures of angles can be positive, negative, or zero.
They can be bigger than 360°.
Basically, they measure an amount of rotation from a fixed direction.
By convention positive means counterclockwise rotation
and
negative means clockwise rotation.

Since you can take the absolute value of any number, and the measures of angles are numbers, you could take the absolute values of them. But you would not be taking the absolute values of the angles. Instead you would be taking the absolute values of the measures of the angles.

I can't think of a situation where that would be useful, but possibly there might be some.

Angles CAN be negative. It certainly matters whether they are positive or negative, if you are navigating across an ocean, for example ! If clockwise is positive, then anticlockwise is negative. +300° and -60° would usually be considered to be the SAME angle, depending upon which position you selected as a starting point.

In any meaningjul context, the notion of "absolute" value is not appropriate when applied to angle measurement. You are throwing away an essential item of information. The result would be meaningless.

Angles are not negative since they range from 0 degrees to 360 degrees.
If you are talking about taking an absolute value of solutions that are negative in regards to angles in functions like sin( θ ), cos( θ ), tan( θ ), etc., only the solution is negative before taking the absolute value, not the angle itself (if that makes sense). It just depends on which function you choose and at what angle you are measuring from.

Look up functions like sin( θ ), cos( θ ), tan( θ ), csc( θ ), sec( θ ), and cot( θ ) and see how they are related to your learning. These functions are very helpful, especially in physics and engineering.

Angles can't be negative, so no