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Geometry/Angles Wider than 360 Degrees

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Question
Why can't there be an angle wider than 360 degrees? Is there such thing as a 3D angle?


Thank you~:)

Answer
Hi Gen!

An angle represents the spread of two lines.  By definition, a circle has 360 degrees (or a "degree" is a 360th of a circle).  Therefore, whenever we have an angle of 360 degrees, we really have the two lines one on top of the other, which is identical to an angle of 0 degrees.  
Another way to see it is like this.  Circles have 360 degrees and any angle can be resolved as a sector of a circle, therefore angles may be no wider than 360 degrees.

As for 3D, angles represent only the spread of two lines.  So if we have some 3D situation, say a javelin planted in the ground, we need two angles to represent it.  First, there is an angle made on the ground between some predetermined axis and the javelin (a top view).  Second, there is a vertical angle between the javelin and the ground (stand parallel to the javelin and measure the angle it makes with the ground).  These two 2D angles comprise what some might call a 3D angle.

Thanks for asking,
Azeem

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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