This is another one of those questions which I can in no wise even begin to
answer, but which I suspect would quickly become a veritable piece o'cake
if I could but see the vector in its coordinate space for only an instant.
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Visually it doesn't make sense for an angle to be negative. However we often measure angles off of some axis, such as the x-axis, and positive angles go around counter-clockwise, while negative angles go around clockwise. Outside of the context of a Cartesian Coordinate system (x-y plane), negative angles don't generally make sense.
For certain angles, the answer is yes. For 30o to the horizontal (in the positive x direction), you need to measure the horizontal distance to be twice the vertical distance. For example, draw a triangle with a base length of 10cm and, at a right angle to the base, measure a height of 5cm. The angle to the horizontal (the smaller angle) will be 30o. (The opposite is true for the angle of 60o).
The x axis is the horizontal (flat, bottom, left-right) axis generally, though sometimes they are manipulated to make math easier. -the x axis sometimes represents time The y axis is the vertical (up-down) one.
Positive + Negative = Negative Negative + Negative = Positive Positive + Positive = Positive Negative + Positive = Negative
Obtuse angle (here is the formula) -: 90° = Right angle and if you don't know the obtuse angle is more than 90° so adding 2 will make it an obtuse angle.