Question

Question on picture attached, easy but i’m stuck (need help asap)

Answer 1

∠CDF = 54

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