Question 11b

∠ FDE (red) = ∠ FDC (blue) - ∠ EDC (green)

∠ EDC (green) = 180 - 135 = 45

∠ DAF = 180 - ∠ DAE (green)

∠ DAE (green) is in parallelogram ABCD

∠ DAE (green) = ∠ DCB = 116° (opposite angle in parallelogram is the same)

∠ DAF = 180 - ∠ DAE (green) = 180 - 116 = 64

∠ FDC (blue) → ∠ ADC (purple) + ∠ FDA (orange)

∠ ADC (purple) → 180 - 116 = 64

AD = FD

▵ ADF is an isosceles triangle

∠ FDA (orange) → 180 - 64 x 2 = 52

∠ FDC (blue) → ∠ ADC (purple) + ∠ FDA (orange) = 64 + 52 = 116

∠ FDE (red) = ∠ FDC (blue) - ∠ EDC (green) = 116 - 45 = 71