Final answer:
The measure of angle BAD in a rhombus with angle BDC equal to 38° should be 71°, considering the properties of a rhombus that opposite angles are congruent and adjacent angles are supplementary. However, this doesn't match any of the provided options.
Step-by-step explanation:
If ABCD is a rhombus and angle BDC = 38°, we are looking for the measure of angle BAD. In a rhombus, opposite angles are congruent and adjacent angles are supplementary. Since angle BDC is one of the interior angles at vertex D, and the angles at each vertex of a rhombus sum up to 180°, the angle ABC must also be 38°. Then angle BAD, being supplementary to angle ABC, is 180° - 38° = 142°. However, we are interested in each half of angle BAD since the diagonals of a rhombus bisect the angles at the vertices. Therefore, the measure of angle BAD is 142° / 2 = 71°.
However, none of the options provided match our finding of 71°, indicating that there might be an error in the options or that we misinterpreted the question. If ABCD is indeed a rhombus and BDC is one of the interior angles at vertex D, then we would expect angle BAD to be 71° based on standard geometric properties of rhombuses.