Measuring Angles: Negatives & Quadrants

Eucliwood
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<Moderator's note: Moved from the welcome forum. General question on the measurement of angles and thus no homework.>

So we have a physics lab and here's the diagram. I do know how to calculate all but i got negative angle. Does that mean that that angle is reference to the negative x quadrant 2? and i can just remove the negative in it?
51635738_1900207886757613_3401633155201892352_n.jpg?_nc_cat=110&_nc_ht=scontent.fmnl6-1.jpg
 

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It is as with all measurements. If you measure your height head to toe, are you negatively tall? So whether you can skip the sign depends on what you want to know: the absolute, i.e. standalone angle, or an angle relative to other angles and measurements. In the latter case you cannot just drop the sign, because ot would destroy the relationship to other angles. Angles are dependent on a coordinate system and thus the choice of the coordinates determine the signs of the angles.
 
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