A ring gear for an epicyclic or planetary reduction gear of a turbomachine, in particular of an aircraft, said ring gear extending about an axis X and comprising first and second coaxial annular elements and comprising, respectively, two inner annular toothing sets of different orientation, each of said toothing sets having a pitch diameter and a median plane substantially perpendicular to said axis and with an intersection point designated Y in an axial cross-section of the ring gear, said first and second annular elements further comprising, respectively, first and second radially outer annular flanges for attaching said first and second elements to each other, wherein each of said first and second flanges comprises a peripheral portion extending in a plane that is angled with respect to said axis X and that passes substantially through said intersection point Y.