Where could I Be ?

If I look at two landmarks (identifiable features with known coordinate) and if I am able to measure the apparent angle between these two points, could I derive my position from that observation ?

No, because there exist a full set of point (called a Locus of point) that will accommodate these parameter.

Locus of point defined by a constant view angle from 2 fixed points.

Set of point defined by the fact that they form a given angle with two fixed points (A et B, of the Euclidian Plane).

NB : Be careful to be coherent with the orientation of your angles, and that the construction is not the same if the angle is acute (<90°) or obtuse (>90°)