An angle-adjustable hinge comprising: a first member holding a disc body having a non-circular through hole as to freely rotate around an oscillation axis, a non-circular shaft portion to be inserted to the through hole, and a second member fixed to an end of the non-circular shaft portion, wherein the first member and the second member are, by insertion of the shaft portion to the through hole, pivotable so as to relatively oscillate, and a gear portion is formed on 1/3 to 1/4 of a peripheral edge portion of the disc body and two protruding portions are formed at the beginning and at the end of the gear portion, a floating wedge member, of which one side is a toothed face engaged to the gear portion and another face is a contact face to contact a wedge face formed on the first member side, wherein relative oscillation of the first member and the second member in a first direction is restricted in an engaged state in which the contact face contacts the wedge face and the toothed face and the gear portion are engaged, wherein the floating wedge member is movable to be part from the gear portion in a retreat state by oscillating the first member and the second member relatively in a second direction to a lock-releasing position (P 0) so as to release the engagement of the gear portion and the toothed face, and wherein the first member and the second member are relatively oscillated in the first direction in the retreat state; the angle-adjustable hinge further comprising a recovery means, which recovers the floating wedge member from the retreat state to the engaged state with the gear portion by a return action (M 2) of a predetermined small angle (θ) in the second direction during free oscillation (M 1) wherein, during free oscillation (M 1), the first member and the second member are relatively oscillated in the first direction from the lock-releasing position (P 0), characterized in that the disc body protrudes circular low protrusions from left and right sides thereof, and is held as to freely rotate by a pair of facing plate portions with the circular low protrusions inserted to the circular supporting holes of the facing plate portions, disposed mutually parallel and fixed to an attachment portion of the first member. a first member holding a disc body having a non-circular through hole as to freely rotate around an oscillation axis, a non-circular shaft portion to be inserted to the through hole, and a second member fixed to an end of the non-circular shaft portion, wherein the first member and the second member are, by insertion of the shaft portion to the through hole, pivotable so as to relatively oscillate, and a gear portion is formed on 1/3 to 1/4 of a peripheral edge portion of the disc body and two protruding portions are formed at the beginning and at the end of the gear portion, a floating wedge member, of which one side is a toothed face engaged to the gear portion and another face is a contact face to contact a wedge face formed on the first member side, wherein relative oscillation of the first member and the second member in a first direction is restricted in an engaged state in which the contact face contacts the wedge face and the toothed face and the gear portion are engaged, wherein the floating wedge member is movable to be part from the gear portion in a retreat state by oscillating the first member and the second member relatively in a second direction to a lock-releasing position (P 0) so as to release the engagement of the gear portion and the toothed face, and wherein the first member and the second member are relatively oscillated in the first direction in the retreat state; the angle-adjustable hinge further comprising a recovery means, which recovers the floating wedge member from the retreat state to the engaged state with the gear portion by a return action (M 2) of a predetermined small angle (θ) in the second direction during free oscillation (M 1) wherein, during free oscillation (M 1), the first member and the second member are relatively oscillated in the first direction from the lock-releasing position (P 0), characterized in that the disc body protrudes circular low protrusions from left and right sides thereof, and is held as to freely rotate by a pair of facing plate portions with the circular low protrusions inserted to the circular supporting holes of the facing plate portions, disposed mutually parallel and fixed to an attachment portion of the first member.