Given: ad and eh , transversal bf ∠acg and are same side interior angles

Step-by-step explanation:By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.

This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.

Then:

By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are same-side interior angles. Because AB and DC are parallel, the same-side interior angles must be supplementary by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.