Select a figure from the given four alternatives which fits exactly into…

Concept: In a "complete the square" figure-formation question, Figure X already occupies part of a square using two of the square's own straight sides; the remaining boundary where the missing piece will join is an irregular staircase-plus-diagonal edge. The correct option must trace that exact staircase-and-diagonal boundary as a mirror path (the option may be drawn in a different orientation, so it may need to be mentally rotated) and must supply the square's other two straight sides, so the two pieces close into one gap-free square.

Application: Figure X has a full vertical left side and a full horizontal bottom side, meeting at the square's bottom-left corner. From the bottom-right corner, its boundary rises in a diagonal, then breaks into a small step (a short notch up, across, and down again) before finally meeting the top-left corner. So the missing piece must supply the square's top and right sides (meeting at the top-right corner) and its own inner edge must reproduce that same diagonal-then-step path, moving from the bottom-right corner up to the top-left corner. Checking each option (rotating as needed so its two straight sides fall on the top and right): Figure (1), turned a quarter-turn, lines up its diagonal and step exactly along Figure X's inner boundary from corner to corner — the two figures close into a complete square with no gap.

Cross-check: Figure (3) matches the step roughly but replaces Figure X's kinked diagonal with one long straight cut, leaving a sliver gap near the bottom-right corner; Figure (4) has its two straight sides on the pair adjacent to (not opposite) Figure X's own straight sides, so its diagonal meets the wrong corner and cannot close the square; Figure (2) has only one clean straight side in any orientation, so it can never supply the two full sides the missing piece needs. Only Figure (1) completes the square exactly.