Let the side length of the regular octagon be 1 unit.
a = ⅛*180(8-2)
a = ⅛(180*6)
a = 135°
a is the single interior angle of the regular octagon.
2b² = 1²
b² = ½
b = ½√(2) units.
c = 1+b
c = (1+½√(2)) units.
c is the side length of the square.
Therefore, the required angle, x is;
tanx = (½√(2))/(1+½√(2))
x = 22.5°
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