You can use the standard sign convention used for giving signs to angles measured based on the rotation of terminal side.
- For figure 1, first and third angles are positive. Second angle is negative.
- For figure 2, first and third angles are negative. Second angle is positive.
- For figure 3, first angle is positive, second one is negative.
How to identify which angle is positive and which angle is negative?
There is a sign convention used internationally by whole mathematics community that whenever the angle will be measured clockwise, it will be taken as negative angle. And whenever the angle will be measured anticlockwise(opposite to how clock's hands move), the angle will be having positive sign.
This was done to differentiate between both methods of measuring the angles (in some context, we need to differentiate, for example, tightening of screws does care about which side you rotate it, so we need some data to differentiate it. Thus, we take help of signs to differentiate between them).
Usually, for constructing angles, we have two lines joined on one point. One side is kept fixed and is called initial side.
Other side is kept non-fixed and it can move. This is called terminal side.
If the terminal side moves like a clock's hands move, then angle measured will be negative, otherwise for anticlockwise (also called counterclockwise) motion, the angle measured will be positive.
Note that as the terminal side stops, we get an angle.
Identifying the sign of given angles in given figure
For figure 1, the first angle and third angle is measured anticlockwise, thus they are positive(see how the arrow goes. Its tip shows from where it came and where it is pointing. It shows that it is moving opposite to how clock's hands move). The second angle is negative because its arrow moves clockwise(thus, the angle is measured clockwise and thus, will have negative sign)
Similarly,
For figure 2, first and third angles are negative. Second angle is positive.
For figure 3, first angle is positive, second one is negative.
Thus,
- For figure 1, first and third angles are positive. Second angle is negative.
- For figure 2, first and third angles are negative. Second angle is positive.
- For figure 3, first angle is positive, second one is negative.
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