Adjacent angle are just that...adjacent to each other. See the bottom link for a visual. So, in general, looking at the upper right rectangular section, adjecent angles are the angle below the red line and the angle above the red line that for the 90 degree angle.

A complementary angle...

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Adjacent angle are just that...adjacent to each other. See the bottom link for a visual. So, in general, looking at the upper right rectangular section, adjecent angles are the angle below the red line and the angle above the red line that for the 90 degree angle.

A complementary angle is one in which two angles sum to 90 degrees. So if you look at an image of the Union Jack flag, you'll see that the flag is basically divided by a large plus sign making four separate rectangular sections, much like the quadrants of an X Y coordinate graph. You'll also notice each rectangular section has a diagonal which creates two separate angles whose sum is 90 degrees.

So, in general, looking at the upper right rectangular section, complimentary angles are the angle below the red line and the angle above the red line that for the 90 degree angle.

Not sure how precise an answer you need, but I've included a link below which may help you see this more clearly.