Final answer:
The measure of angle BAD cannot be accurately determined with the information given, as subtracting m ∠ABC from 360 degrees to find the measure of angle BAD yields 246 degrees, which is not among the options, and there might be an error in the question or missing context.
Step-by-step explanation:
To solve for the measure of angle BAD, we need to understand that the angles around a point total 360 degrees. If we are given that m ∠ABC = 114 degrees, then we can subtract this from 360 degrees to find the measure of angle BAD since they together form a full circle around point B.
So, the calculation we need to perform is:
360 degrees - 114 degrees = 246 degrees
However, the answer is not among the options provided which suggests there might be an error in the question or our understandings. If the angle BAD is adjacent to ABC in a straight line, then they would sum up to 180 degrees, giving us:
180 degrees - 114 degrees = 66 degrees, which also is not among the options provided. Therefore, with the information provided, we cannot accurately determine m ∠BAD and the question may require clarification or additional context.