If angle a measures 57 degrees and angle c is adjacent to angle a, what is the measure of angle c if the two angles are complementary?

33 degrees, 
90-57=33
complementary angles mean that together, the angles add up to equal 90 degrees

The definition of complementary angles is that the sum of two angles should be equal to 90 degrees. We can see that in this case angles A and C are complementary angles. So we can do 90-57 to get 33 and we can see that angle C would equal 33 degrees. Hope this helps. Feel free to ask more questions, or ask questions about my explanation.