Answer:
∠CDF = 54
Step-by-step explanation:
In ΔAEB,
AE ≅ AB
∠ABE = ∠E = x {Angles opposite to equal sides are equal}
∠EAB + ∠E +∠ABE = 180 {angle sum property of triangle}
26 + x + x = 180
26 + 2x = 180
2x = 180 - 26
2x = 154
x = 154/2
x = 77
∠ABE = ∠E = 77
In quadrilateral AECF
∠A + ∠E + ∠C + ∠F = 360
90 + 77 + ∠C + 90 = 360
∠C + 257 = 360
∠C = 360 - 257
∠C = 103
∠FCD + ∠BCD = ∠C
∠FCD + 67 = 103
∠FCD = 103 - 67
∠FCD = 36
ΔFCD,
∠FCD + ∠CDF + ∠CFD = 180
36 + ∠CDF + 90 = 180
∠CDF + 126 = 180
∠CDF = 180 - 126
∠CDF = 54
