Final answer:
The information provided is insufficient to determine the measure of arc AD because there is no clear relationship or context given between angle APE and arc AD.
Step-by-step explanation:
The question asked by the student regarding the measure of arc AD cannot be answered directly because the information provided in the question is either incomplete or not directly related to determining the measure of an arc. The measure of angle APE is given as 67 degrees, but without additional context such as the type of circle or diagram, or the relationship between the angle and the arc, it's not possible to determine the measure of arc AD. In geometry, if angle APE is a central angle, then the measure of arc AD would be equal to the measure of the central angle. However, without a clear diagram or additional information, we can only provide general guidelines.