As shown in the figure, the points m and N are on the sides BC and CD of the square ABCD respectively. It is known that the perimeter of △ MCN is equal to half of the perimeter of the square ABCD, then ∠ man=______ ．

When △ adn is rotated 90 ° clockwise around point a, we can get △ Abe,  AE = an, be = DN,  Abe =  d = 90 degree,  NAE = 90 degree and  ABC = 90 degree,  points m, B and E are collinear,  me = be + BM = DN + BM,  MCN's perimeter is equal to half of square ABCD's perimeter,  Mn + NC + MC = DC + BC = DN + NC + MC + BM,  Mn = DN + BM,  Mn = me. In △ man and △ Mae, an = aemn = meam = am,  ma N ≌ △ MAE (SSS), ≠ Nam = ∠ EAM, ∈ man = 12 ∠ NAE = 45 °. So the answer is 45 °

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