ΔBDA should = 180°
∠D + 60 + 50 = 180
∠D + 110 = 180
∠D + 110 (-110) = 180 (-110)
∠D = 70
Due to vertical angles (theorem?), the ∠FDE is also 70°
to find ∠DFE, find ∠BDF
∠BDF = 180 - 70 (this 70 is from ∠D)
∠BDF = 110
∠BFD = 180 - 110 - 20
∠BFD = 50
∠D = 70
ΔFDE = x + 70 + ∠F
ΔAD'E = 180
∠D' = 70
∠DFC = 110
angle bisector states that it makes two equal angles
110/2 = 55
∠DFE= 55
180 - 70 - 55 =
180 - 125 =
55
x = 55°
I'm hoping that this is right
& hope this helps
