Final answer:
The information provided is insufficient to determine the measure of angle ACE in the triangle, as essential details about the triangle or the relationship between angles are missing.
Step-by-step explanation:
The question is about solving for the measure of angle ACE in a triangle geometry problem. Given angle DEB = 8x + 32 and angle ACE = 4x + 44, we are supposed to find the value of angle ACE. Unfortunately, the provided information in the question seems incomplete or unclear as we would require more details about the relationship between angles and lines in the triangle to provide a solution. In a typical geometry problem involving midpoints and angles, we would use triangle properties such as the angles adding up to 180 degrees in a triangle or properties about isosceles or equilateral triangle to find the missing angles but in this case, crucial information for doing so is missing. Thus, without additional information or a correct diagram, a solution cannot be accurately determined.