In the given diagram, angles AEG and CEG are complementary, forming a total of 90 degrees. CEG and CEB are not complementary.
In the given diagram, since angle CEB is 90 degrees, it forms a right angle. Complementary angles add up to 90 degrees. Looking at the options:
a. angle AEF and FED: These angles are adjacent and form a straight line, so they are supplementary, not complementary. FED and DEB: The sum of these angles is not 90 degrees.
b. angle AEF and FED: These angles are adjacent and form a straight line, so they are supplementary. AEG and CEG: These angles add up to 90 degrees and are complementary.
c. angle AEG and AED: The sum of these angles is not 90 degrees. FED and DEB: The sum of these angles is not 90 degrees.
d. angle AEG and CEG: These angles add up to 90 degrees and are complementary. CEG and CEB: The sum of these angles is not 90 degrees.
Therefore, the correct answer is option d: angle AEG and CEG, which are complementary angles, and CEG and CEB are not complementary.