Angles in a folded figure

A B C D is a rectangular piece of paper. It is folded along the dotted line A E. Angle A E D is 58 degrees. Find angle x. Try it first. Pause if you like. The dotted line A E is the crease, and it is a line of symmetry. Fold along it and the two sides land exactly on each other. The corner that moved is written D prime. It is the same corner of the same paper, in a new place. That corner was a right angle, and after the fold it is a right angle. So a fold does not change the size of an angle. x sits in corner A, beside the folded edge. The angle next to it is the fold's copy of angle D A E, so we find angle D A E first. In triangle A D E, corner D is a right angle, and angle A E D is 58 degrees. So angle D A E is one hundred and eighty minus 90 minus 58, which is 32 degrees. The bracket names the property: angle sum of a triangle. Now cross the crease. Angle D prime A E is the folded copy of angle D A E, so it is 32 degrees as well. The double arcs mark the two angles equal. And the bracket says why: folded angles are equal. Corner A of the rectangle is a right angle, and three angles share it. Angle D A E, the folded copy beside it, and x. So x is 90 minus 32 minus 32, which is 26 degrees. The bracket names it: right angle of a rectangle. x is what is left of corner A. The two 32s are one angle, drawn on both sides of the crease. The right angle at D is the right angle at D prime. A fold is a change of place, not a change of size.