Angle DEF and angle FEG are supplementary. The measure of angle DEF = (9x + 1) and the measure of angle FEG = (8x + 9). What is the measure of angle FEG?

Supplementary angles are angles that are adjacent to each other and when summed to get a total of 180 degrees. In this case, DEF and FEG are supplementary. Thus the equation is 9x + 1 + 8x + 9 = 180 = 17 x + 10; x then is equal to 10 so

< DEF = 9*10 + 1 = 91 degrees