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Kmieteczka
ABCDEF is a regular hexagon so every angle is even. 

A sum of degrees of all internal angles = (n-2)×180°
n - the number of angles

S = (6-2)×180°
S = 4 × 180°
S = 720°

One angle in the hexagon = 720°:6 = 120°
∡DEF = ∡ABC = 120°
The triangles DEF and ABC are isosceles triangles, so:
∡BAC = ∡BCA = ∡EDF = ∡EFD = (180°-120°):2 = 30°

∡AFD + ∡EFD = 120°
∡AFD = 120° - ∡EFD
∡AFD = 120° - 30°
∡AFD = 90°

Do the same with other angles.


 :)

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