Tire with asymmetrical and reinforced sidewalls

A tire comprising two beads, a crown provided with a tread and first and second sidewalls connecting said crown to said beads, said beads comprising radially on the inside portions which make an angle open axially and radially outwards and intended to be in contact with a rim comprising rim seats inclined at an angle γ which is also open axially and radially outwards, said tire being reinforced by a carcass reinforcement comprising at least one carcass ply formed of reinforcements parallel to one another in the ply and making an angle α relative to the circumferential direction such that 60°≦α≦90°, said reinforcement being anchored in each bead to at least one annular anchoring element, and the carcass reinforcement being surmounted radially by a crown reinforcement itself surmounted by the tread,

• the first and second sidewalls each having an additional, inextensible ring located axially inside the axially outermost carcass ply,
• the line segment passing through the center of gravity G8 of the section of the ring in the first sidewall and through the anchoring ring in the bead located in the extension of said first sidewall making an angle β1 with the rotation axis which is open towards the outside,
• the line segment passing through the center of gravity G8′ of the section of the ring in the second sidewall and through the anchoring ring in the bead located in the extension of said second sidewall making an angle β2 with the rotation axis which is open towards the outside,
• each sidewall comprising a coupling section located radially between the additional ring and the annular anchoring element in the bead, said tire, when mounted on its service rim and inflated to the recommended pressure, wherein, as viewed in meridian section, the angle β1 is different from the angle β2.