we can find coterminal angles if we simply transverse a full revolution in the positive direction or the negative direction. That is, simply add 360° (positive direction) or subtract 360° (negative direction). Why does this work? please  explain and justify the reasoning.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.CR: Review Exercises
Problem 47CR
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we can find coterminal angles if we simply transverse a full revolution in the positive direction or the negative direction. That is, simply add 360° (positive direction) or subtract 360° (negative direction). Why does this work? please  explain and justify the reasoning.

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