On the complete upper angle about a point on the Minkowski plane

The dependence of the complete upper angle in the sense of A. D. Aleksandrov about a point on the Minkowski plane on the form of the “unit circle” (the centrally symmetric convex curve $\Phi$ determining the Minkowski metric $\rho_{\Phi}$) is studied. The complete upper angle is computed in three cases: if $\Phi$ is a square, a “cut circle,” or a “rounded rhombus”.