Let M be a maximal subgroup of a finite group G. A pair of subgroups (C,D) of G is called a theta-pair of M if it satisfies the following conditions: (i) D < C and D is normal in G, (ii) = G, = M and (iii) C/D has no proper normal subgroup of G/D. In this paper, we introduce the degree of maximal theta-pairs denoted by dtheta_m(G) as the ratio |\theta_m(G)|/|G|, where theta_m(G) is the set of all maximal theta-pairs of the maximal subgroups of G and m(G) is total number of distinct maximal subgroups of G. Moreover, we obtain some result on the degree of -pairs and solvability and nilpotancy of finite groups.
