A dual-opening carton has a front, rear, and opposing side panels. A flap extends over the top of the carton, allowing the top to be opened and re-closed. A score line extends around the carton to facilitate the removal of a top portion of the carton. The score line has segments extending along the front panel, the rear panel, and rear portions of the side panels that have a relatively low cut length to land length ratios that maintain relatively high structural integrity. The score line also has segments extending along the front of the side panels have a relatively high cut length to land length ratio to facilitate tear propagation. The score line extending along the side panels is angled so that a pull force vector removing the top portion of the carton runs along a plane generally parallel to the score line.