Final answer:
Without additional context or measurements, it is not possible to accurately order the given angles and sides from least to greatest.
Step-by-step explanation:
To order both the angles and sides from least to greatest, we need to rely on facts about the properties of angles and sides in geometry. For the angles, we can use the transitive property, which states that if angle A is greater than angle B, and angle B is greater than angle C, then angle A is definitely greater than angle C.
The same applies to the sides of triangles, where the triangle inequality theorem can help us determine the order. However, without specific measurements or relationships between the angles and sides in the question, we cannot accurately order them. The fragments of information provided, such as the sum of angles in a triangle equaling 180 degrees, do not relate directly to the angles given (∠B, ∠C, ∠BDC). Similarly, the lengths of sides DE, EF, and DF cannot be ordered without additional context.
If by chance there was a triangle involved and ∠B and ∠C were inside the triangle with ∠BDC being an exterior angle to the vertex containing ∠C, then ∠BDC would be greater than ∠C, which would be greater than ∠B if ∠B is opposite the smallest side. But again, without proper context, defining an order is impossible.
For the sides, if DE, EF, and DF are sides of a triangle, then we can say DE + EF > DF, DE + DF > EF, and EF + DF > DE according to the triangle inequality theorem. Yet, without actual values, this information is not sufficient to order the sides given.