Answer:
Option D
∠GDE is supplementary to ∠DEF and also supplementary to ∠FGD
Step-by-step explanation:
To use the supplementary property to identify a parallelogram. The condition must be that that the same-side interior angles (consecutive angles) are supplementary.
Thus for parallelogram DEFG
D --------------------E
/ /
G---------------------F
Thus, we have it that the condition that is most sufficient to show that quadrilateral DEFG is a parallelogram is
∠GDE is supplementary to both ∠DEF and ∠FGD
