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When a particle moves with constant velocity, no external force acts on it. To produce torque and hence to change angular momentum we need some transversal force which is not acting and hence angular moment remains constant.
Also ang. mom = mvr
where r is the perpendicular distance from origin(in thus case) to the direction of motion, which constant as the particle is moving along a straight line. m and v are constant in problem. Thus angular momentum is constant.
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