What is an alternative form of measuring angles?

Question

compare it with the degree measure and include the origin, applications, benefits or drawbacks.

Answer 1

In the sentence Using a protractor gets you the exact angle measure of an orientation, I think that the word EXACT is not technically correct. Good instruments will be able to provide good measurements, but when it comes to reading fractions of an angle on a protractor, the best we can say is that we're limited by the eyeballs & judgment. 

 

Physical measurements of this kind are empirical, and never can be exact.

Answer 2

An alternative way (other than using protractor) is using inverse trigonometry.  Using a protractor gets you the exact angle measure of an orientation.  Using inverse trigonometry gets you a scaled angle that you can use as a reference value for the actual angle measure.

 

When using a protractor, you are measure the angle of an actual object.

When using inverse trigonometry, you are using a scaled diagram of the actual object to calculate the angle.

 

This alternative form is used for architecture and construction projects.  Because a protractor is too small to measure an object that is very large in size.