Calculating the red angle (angle DAM).
Notice!
ABCD is a regular quadrilateral (square).
Let AB be 1 unit.
tan60 = AB/BK
BK = 1/√(3)
BK = ⅓√(3) units.
CK = 1-BK
CK = ⅓(3-√(3)) units.
tan30 = CK/CM
CM = √(3)*⅓(3-√(3))
CM = ⅓(3√(3)-3)
CM = (√(3)-1) units.
DM = 1-CM
DM = 1-(√(3)-1)
DM = (2-√(3)) units.
Therefore, the required angle, angle DAM is;
Let it be x.
tanx = DM/AD
tanx = (2-√(3))/1
x = atan(2-√(3))
x = 15°
Where x is the required angle, angle DAM.
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