When are angles negative? In earlier grades we learnt that in for instance an equilateral triangle all angles are 60 degrees. Now in high school I am taught that measuring angles anti-clockwise and clockwise make a difference.

So does that mean in an equilateral triangle one angle is 60 which is measures anti-clockwise and one is -60 degrees which is clockwise and.. I don't know, I am pretty confused.

How does it add to 180 then?

I was taught about this negative angle concept in trigonometry in unit circles which I understood very well but why is it if not applicable to any geometric figure?

It looks like I am lacking some common sense.
The following line segment on the number line has length four.

    ---------
0 1 2 3 4 5 6 7


The following arrow drawn on the number line represents a displacement of $-4$.

    &lt;--------
0 1 2 3 4 5 6 7


The following arrow drawn on the number line represents a displacement of $4$.

    --------&gt;
0 1 2 3 4 5 6 7


You can do the same thing with angles; sometimes you only care about the magnitude, but other times you pick an orientation: you decide which leg of the angle you start at and which leg you end at. When we orient angles, we typically pick counterclockwise to be the positive direction, and clockwise to be the negative direction.

Even more interesting is an idea of angular position versus angular displacement. If we consider an angle whose vertex is the origin and one leg (the starting leg) is the positive $x$ axis, then putting the other leg at $270^\circ$ would be the negative $y$ axis, but $-90^\circ$ would also be the negative $y$ axis.

The idea that $270^\circ$ and $-90^\circ$ represent the same angle is the idea of angular position.

However, there is a difference between actually going counterclockwise $270^\circ$ around the plane from the positive $x$ axis to the negative $y$ axis, and going $90^\circ$ clockwise (i.e. $-90^\circ$ counterclockwise) from the positive $x$ axis to the negative $y$ axis. When this difference matters, we call it "angular displacement". We could even consider going completely around the origin to return to the $x$ axis then continuing another three quarters the way around: this would be a displacement of $630^\circ$!



As an addendum, if we orient the two legs of the angle so that they point in opposite directions in relation to the vertex, then we usually consider the leg pointing away from the vertex to be the starting leg, and the leg pointing towards the vertex to be the ending leg.

This way, if we orient the three sides of a triangle so that the sides all point in a counter-clockwise direction around the triangle, then all of the angles are oriented counter-clockwise too.
Angle is a measurement and can't be negative, and it is used to define a certain point on the trigonometric circle. In the trigonometric circle, counterclockwise rotation is denoted the positive sign and counterclockwise is denoted the negative sign. for example, moving 60 degrees in the positive direction is completely identical to moving 300 degrees in the negative direction, as they both define one point.
Note that the choice of + or - is completely arbitrary and makes no difference; what really matters is the absolute value of angular displacement.