What is a non-constant angle measurement?

Question

I read in my textbook that radian is a constant angle.

What does it mean for an angle to be constant?
Are degree and grade constant angles as well?
What angles are non-constant?

PS : I'm just a beginner in angles, let me know if this is a silly question

Thanks

Answer 1

If three sides lengths in a triangle are equal then each angle is constant at $60^{\circ}$.

Any angle turned in the plane can be expressed either in degrees or radians.It is a measure of rotation.

If one side is made of thin flexible plastic and you bend it so everywhere it has same distance from the opposite vertex making a circle arc, then the opposite angle reduces by a couple of degrees and a bit more approximately to $57.3^{\circ}$, a famous constant and theoretically useful angle called the radian.

If you take a right or left turn you execute a constant 90 degree angle or $\pi/4$ radian.

And full turn means 360 degrees or $2\pi$ radians.

etc.