The authors study some properties of the Newton polygon \(N(f)\) of a polynomial \(f\) with complex coefficients. They obtain estimations for the angular distribution of the roots of \(f\), including improvements of results of \textit{M. Marden} [The geometry of the zeros of a polynomial in complex variables (AMS Surveys 3) (1949; Zbl 0038.153)]. There are used the Newton polygons of polynomials associated with \(f\) and a result of \textit{A. Khovanskij} [C. R. Acad. Sci., Paris, Sér. A 292, 937-940 (1981; Zbl 0488.32001)]. Among the applications we mention the estimation of the area in \(\mathbb{R}^ 2\) of points \((u,v)\) with \(| F(u,v)|\leq 1\), where \(F(u,v)\) is the homogeneous form associated with \(f\). The bounds obtained for this area are dependent on the structure of \(N(f)\).