Let the side length of the regular pentagon be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is the side length of the square.
sin18 = b/1
b = 0.30901699437 units.
cos18 = c/1
c = 0.9510565163 units.
d = 1.61803398875-0.9510565163
d = 0.66697747245 units.
e = 1.61803398875-0.30901699437
e = 1.30901699438 units.
It implies, the required angle x° is;
tanx = 0.66697747245/1.30901699438
x = 27°
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