Two angles are complementary if their measures add up to 90 degrees and are sumpplementary if their measures add up to 180 degrees.
From the image, we notice that the angles:
These angles add up to 180 degrees because line JG bisects line HE at a 90 degrees angle, therefore, they are supplementary.
For angles
These angles are supplementary because their measures add up to 180 degrees.
For angles:
These are neither supplementary nor complementary because line GD is not a straight line.
For angles:
We have the following relationship for these angles:
Since angle GJH is 90 degrees we have:
Subtracting 90 to both sides:
Therefore, their sum is 90 degrees and therefore they are complementary.