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Angled tile collision

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For some reason, I can't get this to work. I have some angled tiles in a tile based platforming game. When the character reaches the "edge" of the tile, he jumps drastically. I'm pretty sure it's because his x tile location has changed, but his y tile location remains the same. But I can't figure out how to fix this.

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I'm not sure how your system works, but I know mine kept track of the x,y tile(s) that the character is associated with at any point in time and as the character moved up a slope, the character's vertical position for example, was adjusted by, first pretending the character is actually in an unoccupied tile location above that and adjusting the y_offset based on the x_offset into a tile. I'm not sure what's happening, but if it worked liked this, you'd have to remember to reset the xtra y_offset every time a tile change occurs.

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