46B20, 46C15, 51K05.

It is known that in a strictly convex normed space, the orthogonality (Birkhoff orthogonality) has the property, ``orthogonality is unique to the left``. Using this property, we introduce the definition of the so-called angle between two vectors, in a smooth and uniformly convex space. Also, we define the so-called angle between two vectors. It is demonstrated that the angle in a unilateral triangle, in a quasi-inner product space, is . The angle between a side and a diagonal, in a so-called quandrangle, is .