In this work, optimum transmit power allocation in V2X networks to maximize the aggregate data rate in the V2I network without violating individual peak transmit power constraints on the V2I users and the interference power constraints on the V2V users is considered. In the proposed model, V2I users form a multiple-access channel to the roadside unit and cause interference in the V2V network. Under this setup, it is first shown that the data rate maximizing optimum power allocation vector lies at one of the vertices of the feasible set of all transmit power vectors. The structure derived for the optimum power allocation vectors simplifies the solution of the power optimization problem significantly. That is, calculating and comparing the data rates at the vertices of the feasible power set, the optimum power allocation vector can be derived for each channel state. Furthermore, with the entry of each new V2V user to the system, the number of vertices increases at most by 3. Time division multiple access solution as a special case appears by a subset of our solution. In the final part of the paper, the theoretical results obtained are utilized to give numerical performance figures for V2X networks.